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--- 分析与偏微分方程讨论班(2021秋季第5讲)

题目: Global stability and non-vanishing vacuum state phenomena of large solutions to 3D isentropic compressible Navier-Stokes equations

报告人: 姚磊  教授 （西北大学）

时间： 2021-11-08 14：30-15：30 (周一下午)

地点: 腾讯会议 ID：870 379 223

腾讯会议链接：

https://meeting.tencent.com/dm/1WCIVGdZ5jZU

摘要: We investigate the global stability of large solutions to the isentropic compressible Navier-Stokes equations in dimension three under periodic boundary conditions. Under the assumption that $\rho$ is essentially bounded, we prove that the solutions convergence to the equilibrium state exponentially in $L^2$-norm. By utilizing some new thoughts, we also show that the density convergences to the equilibrium state exponentially in $L^\infty$-norm if the uniformly lower bound of the initial density is positive. By a product, we prove that the vacuum state is preserved for any time if initial vacuum state appears. This is joint work with Guochun Wu and Yinghui Zhang.

报告人简介: 姚磊，西北大学教授，博士生导师，2010年在华中师范大学获理学博士学位；曾获全国百篇优秀博士学位论文奖、陕西省杰出青年科学基金、陕西省青年科技新星。主要从事流体力学中的偏微分方程数学理论的研究，论文发表在 Math. Ann.、JMPA、Ann. I. H. Poincaré-AN、SIAM JMA、JMFM、JDE等期刊上。

邀请人：郑孝信

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