The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove...The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.展开更多
This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time unifo...This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.展开更多
We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By...We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions,we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain.We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains,and derive some uniform bounds of higher order norms,which are independent of the size of the bounded domains.Then we prove the local existence of unique strong solution of the problem in the exterior domain,provided that the initial data satisfy a natural compatibility condition.展开更多
In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in s...In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.展开更多
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate...We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the follo...The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense： we extend the class of pressure functions, that is, we consider lower exponent γ.展开更多
We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for shor...We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for short) classical incompressible Navier-Stokes equations and using techniques developed in(SIAM J Math Anal, 2020, 52(2): 1806–1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part Pu_0 and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.展开更多
This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of th...This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.展开更多
We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably sm...We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.展开更多
In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum...In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.展开更多
This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational fo...This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.展开更多
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditi...We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.展开更多
In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity ...In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.展开更多
In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case...In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.展开更多
In this paper,we derive several new sufficient conditions of the non-breakdown of strong solutions for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equa...In this paper,we derive several new sufficient conditions of the non-breakdown of strong solutions for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations.First,it is shown that there exists a positive constantεsuch that the solution(ρ,u,θ)to the full compressible Navier-Stokes equations can be extended beyond t=T provided that one of the following two conditions holds:(1)ρ∈L^(∞)(0,T;L^(∞)(R^(3)),u∈L^(p,∞)(0,T;L^(q,∞)(R^(3)))and ||u||_(L^(p,∞)(0,T;L^(q,∞)(R^(3))))≤ε,with 2/p+3/q=1,q>3;(0.1)(2)λ<3μ,ρ∈L^(∞)(0,T;L^(∞)(R^(3)),θ∈L^(p,∞)(0,T;L^(q,∞)(R^(3)))and ||θ||_(L^(p,∞)(0,T;L^(q,∞)(R^(3))))≤ε,with 2/p+3/q=1,q>3/2(0.2)To the best of our knowledge,this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid.Second,we establish some blow-up criteria in anisotropic Lebesgue spaces for the finite blow-up time T^(*):(1)assuming that the pair(p,q) satisfies 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1<q_(i)<∞)and (1.17),then lim sup_((t→T*))||ρ||_(L^(∞)(0,t;L^(∞)(R^(3))))+||u||_(Lp(0,t;L_(1)^(q_(1))L_(2)^(q_(2))L_(3)^(q_(3))(R^(3)))))=∞;(0.3)(2)letting the pair(p,q)satisfy 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1<q_(i)<∞)and(1.17),then lim sup (t→T*)||ρ||_(L^(∞)(0,t;L^(∞)(R^(3))))+||θ||_(Lp(0,t;L_(1)^(q_(1))L_(2)^(q_(2))L_(3)^(q_(3))(R^(3)))))=∞=∞,(λ<3μ).(0.4)Third,without the condition on p in(0.1)and(0.3),the results also hold for the 3 D nonhomogeneous incompressible Navier-Stokes equations.The appearance of a vacuum in these systems could be allowed.展开更多
For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are...For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.展开更多
This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R^2,which studies the existence of solution,and gets the existence of the attractors.Finally,we discuss with limit-behavior of th...This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R^2,which studies the existence of solution,and gets the existence of the attractors.Finally,we discuss with limit-behavior of the Navier-stokes equation4 with nonlinear per-turbation,asα→0.展开更多
Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.
文摘The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.
基金partially supported by the National Natural Science Foundation of China(11701192)。
文摘This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.
基金supported by NSFC(11421061)by National Science Foundation of Shanghai(15ZR1403900).
文摘We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions,we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain.We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains,and derive some uniform bounds of higher order norms,which are independent of the size of the bounded domains.Then we prove the local existence of unique strong solution of the problem in the exterior domain,provided that the initial data satisfy a natural compatibility condition.
文摘In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.
基金supported by National Natural Science Foundation of China (11001090)the Fundamental Research Funds for the Central Universities(11QZR16)
文摘We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
基金supported by National Natural Science Foundation of China-NSAF(11271305,11531010)the Fundamental Research Funds for Xiamen University(201412G004)supported by National Natural Science Foundation of ChinaNSAF(11271305,11531010)
文摘The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense： we extend the class of pressure functions, that is, we consider lower exponent γ.
基金Zhai was partially supported by the Guangdong Provincial Natural Science Foundation (2022A1515011977)the Science and Technology Program of Shenzhen(20200806104726001)+1 种基金Zhong was partially supported by the NNSF of China (11901474, 12071359)the Exceptional Young Talents Project of Chongqing Talent (cstc2021ycjh-bgzxm0153)。
文摘We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for short) classical incompressible Navier-Stokes equations and using techniques developed in(SIAM J Math Anal, 2020, 52(2): 1806–1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part Pu_0 and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.
基金supported by the Program for New Century Excellent Talents in University of the Ministry of Education(NCET-13-0804)NSFC(11471127)+3 种基金Guangdong Natural Science Funds for Distinguished Young Scholar(2015A030306029)The Excellent Young Teachers Program of Guangdong Province(HS2015007)Pearl River S&T Nova Program of Guangzhou(2013J2200064)supported by the General Research Fund of Hong Kong,City U 104511
文摘This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.
基金supported by National Natural Science Foundation of China(11701193,11671086)Natural Science Foundation of Fujian Province(2018J05005,2017J01562)+3 种基金Program for Innovative Research Team in Science and Technology in Fujian Province University Quanzhou High-Level Talents Support Plan(2017ZT012)supported by National Natural Science Foundation of China(11901474)the Chongqing Talent Plan for Young Topnotch Talents(CQYC202005074)the Innovation Support Program for Chongqing Overseas Returnees(cx2020082).
文摘We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.
基金partially supported by the National Natural Science Foundation of China (11671273 and 11931010)key research project of the Academy for Multidisciplinary Studies of CNU and Beijing Natural Science Foundation (1192001).
文摘In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.
基金Program for New Century ExcellentTalents in University(NCET-04-0745)the Key Project of the National Natural Science Foundation of China(10431060)
文摘This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.
基金supported in part by the National Science Foundation under Grants DMS-0807551, DMS-0720925, and DMS-0505473the Natural Science Foundationof China (10728101)supported in part by EPSRC grant EP/F029578/1
文摘We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.
基金supported by China Postdoctoral Science Foundation(2012M520205)supported by National Natural SciencesFoundation of China(11171229,11231006)Project of Beijing Chang Cheng Xue Zhe
文摘In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ（ρ） = ρ^β with β≥0. Note that the initial data can be arbitrarily large to contain vacuum states.
基金supported by NNSFC(11101145),supported by NNSFC(11326140 and11501323)China Postdoctoral Science Foundation(2012M520360)+1 种基金Doctoral Foundation of North China University of Water Sources and Electric Power(201032),Innovation Scientists and Technicians Troop Construction Projects of Henan Provincethe Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313)
文摘In this paper, we investigate the free boundary value problem （FBVP） for the cylindrically symmetric isentropic compressible Navier-Stokes equations （CNS） with density- dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.
基金supported by the NationalNatural Science Foundation of China(11971446,12071113,11601423,11771352,11871057,11771423,11671378,11701145)Project funded by China Postdoctoral Science Foundation(2020M672196)。
文摘In this paper,we derive several new sufficient conditions of the non-breakdown of strong solutions for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations.First,it is shown that there exists a positive constantεsuch that the solution(ρ,u,θ)to the full compressible Navier-Stokes equations can be extended beyond t=T provided that one of the following two conditions holds:(1)ρ∈L^(∞)(0,T;L^(∞)(R^(3)),u∈L^(p,∞)(0,T;L^(q,∞)(R^(3)))and ||u||_(L^(p,∞)(0,T;L^(q,∞)(R^(3))))≤ε,with 2/p+3/q=1,q>3;(0.1)(2)λ<3μ,ρ∈L^(∞)(0,T;L^(∞)(R^(3)),θ∈L^(p,∞)(0,T;L^(q,∞)(R^(3)))and ||θ||_(L^(p,∞)(0,T;L^(q,∞)(R^(3))))≤ε,with 2/p+3/q=1,q>3/2(0.2)To the best of our knowledge,this is the first continuation theorem allowing the time direction to be in Lorentz spaces for the compressible fluid.Second,we establish some blow-up criteria in anisotropic Lebesgue spaces for the finite blow-up time T^(*):(1)assuming that the pair(p,q) satisfies 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1<q_(i)<∞)and (1.17),then lim sup_((t→T*))||ρ||_(L^(∞)(0,t;L^(∞)(R^(3))))+||u||_(Lp(0,t;L_(1)^(q_(1))L_(2)^(q_(2))L_(3)^(q_(3))(R^(3)))))=∞;(0.3)(2)letting the pair(p,q)satisfy 2/p+1/q_(1)+1/q_(2)+1/q_(3)=1(1<q_(i)<∞)and(1.17),then lim sup (t→T*)||ρ||_(L^(∞)(0,t;L^(∞)(R^(3))))+||θ||_(Lp(0,t;L_(1)^(q_(1))L_(2)^(q_(2))L_(3)^(q_(3))(R^(3)))))=∞=∞,(λ<3μ).(0.4)Third,without the condition on p in(0.1)and(0.3),the results also hold for the 3 D nonhomogeneous incompressible Navier-Stokes equations.The appearance of a vacuum in these systems could be allowed.
基金Sponsored by National Natural Science Foundation of China (10431060, 10329101)
文摘For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.
基金Project supported by the Baoshan College focuses on cultivating disciplines of China(Conservative government[2016]No.91)The work was supported in part by the Joint Special Foundation on basic research in Local Colleges and Universities for the Department of Science and Technology of Yunnan Province of China under Grant No.2017FH001-106+2 种基金the Natural Science Foundation of Anhui Province of China(1908085MG233)Quality Engineering for Research Projects of the Anhui Department of Education about Wisdom Classroom(2018zhktl80)Natural Science Foundation for the Higher Education Institutions of Anhui Province of China(KJ2019A0945).The authors would like to thank all the individuals in China who offered their time and energy to participate in the investigates。
文摘This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R^2,which studies the existence of solution,and gets the existence of the attractors.Finally,we discuss with limit-behavior of the Navier-stokes equation4 with nonlinear per-turbation,asα→0.
基金the NNSF of China(107711597)the NNSF of Gansu(3ZS041A25-006)
文摘Using a new method developed in [5], we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in H^3per（Ω） and H^4per（Ω）.
