报告题目：Global stability and non-vanishing vacuum states of 3D compressible Navier-Stokes equations

报告人：姚磊 (西北大学)

报告时间：2022年1月20日（星期四）下午14：00-15：00

报告地点：腾讯会议                会议ID：336 776 345

校内联系人：王文栋 教授        联系电话：84708351-8139

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.

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。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等国际期刊上。主持国家自然科学基金面上项目两项，参加国家自然科学基金重点项目两项。