摘要
主要研究一维可压缩等熵 Navier-Stokes 方程稀疏波在流近似下的零耗散极限问题.若对应的 Euler 方程的稀疏波解的一端与真空连接,本文采用流近似方法控制稀疏波中由真空引起的退化,并构造此可压缩等熵 Navier-Stokes方程的一列解,进而运用基本能量方法证明随着黏性的消失,此列解收敛于 Euler 方程的稀疏波解,且得到一致收敛率.
The paper studies the ux approxomation to the zero dissipation limit to rarefaction wave for the one-dimensional compressible isentropic Navier-Stokes equations. Given that the solution of the corresponding Euler equations is rarefaction wave with one-side vacuum state, we employ the ux approximation method to control the degeneracies caused by the vacuum in the rarefaction wave, and we construct a sequence of solutions to the compressible isentropic Navier-Stokes equations, then we adopt the elementary energy method to prove that the solutions converge to the rarefaction wave as the viscosity vanishes. In addition, the uniform convergence rate is obtained.
作者
王金妮
刘进静
Wang Jinni;Liu Jinjing(School of Mathematics, Northwest University, Xi′an 710127, China)
出处
《纯粹数学与应用数学》
2019年第3期287-306,共20页
Pure and Applied Mathematics
基金
国家自然科学基金(11801444)
作者简介
王金妮(1991-),硕士研究生,研究方向:偏微分方程.
