讲座简介：

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. 

讲座人简介：

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。