## Global stability and non-vanishing vacuum states of 3D compressible Navier-Stokes equations

• 讲座人: 姚磊
• 讲座日期: 2021-11-26
• 讲座时间: 09:00
• 地点: 腾讯会议703328369

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.