This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated proces...This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.展开更多
This study addresses long-time behavior for a thermoelastic microbeam problem with time delay and the Coleman-Gurtin thermal law,the convolution kernel of which entails an extremely weak dissipation in the thermal law...This study addresses long-time behavior for a thermoelastic microbeam problem with time delay and the Coleman-Gurtin thermal law,the convolution kernel of which entails an extremely weak dissipation in the thermal law.By using the semigroup theory,we first establish the existence of global weak and strong solutions as well as their continuous dependence on the initial data in appropriate function spaces,under suitable assumptions on the weight of time delay term,the external force term and the nonlinear term.We then prove that the system is quasi-stable and has a gradient on bounded variant sets,and obtain the existence of a global attractor whose fractal dimension is finite.A result on the exponential attractor of the system is also proved.展开更多
基金partially supported by the Natural Science Foundation of China(11671134)
文摘This paper investigates the pullback asymptotic behaviors for the non-autonomous micropolar fluid flows in 2D bounded domains. We use the energy method, combining with some important properties of the generated processes, to prove the existence of pullback exponential attractors and global pullback attractors and show that they both with finite fractal dimension. Further, we give the relationship between global pullback attractors and pullback exponential attractors.
基金supported by the National Natural Science Foundation of China (11771216 and 11901306)the Key Research and Development Program of Jiangsu Province (Social Development)(BE2019725)the Natural Science Foundation of Jiangsu Province (SBK2017043142)
文摘This study addresses long-time behavior for a thermoelastic microbeam problem with time delay and the Coleman-Gurtin thermal law,the convolution kernel of which entails an extremely weak dissipation in the thermal law.By using the semigroup theory,we first establish the existence of global weak and strong solutions as well as their continuous dependence on the initial data in appropriate function spaces,under suitable assumptions on the weight of time delay term,the external force term and the nonlinear term.We then prove that the system is quasi-stable and has a gradient on bounded variant sets,and obtain the existence of a global attractor whose fractal dimension is finite.A result on the exponential attractor of the system is also proved.
