Global classical solution to 3D compressible Navier-Stokes equations with vacuum
数学专题报告
报告题目(Title)：Global classical solution to 3D compressible Navier-Stokes equations with vacuum
报告人(Speaker)：朱长江 教授，华南理工大学
地点(Place)：教七楼204教室
时间(Time)：2024年5月27日上午10:30--11:30
邀请人(Inviter)：许孝精
报告摘要
In this talk, we establish the existence of global classical solution to 3D Cauchy problem of the isentropic compressible Navier-Stokes equations with large initial data and vacuum under the assumption that $(\gamma-1)^\frac{1}{6}E_0^{\frac{1}{2}}\mu^{-\frac{1}{2}}$ is suitably small. It is showed that the initial energy $E_0$ can be large if the adiabatic exponent $\gamma$ is near $1$ or the viscosity coefficient $\mu$ is taken to be large. Moreover, when $\gamma=1$, we also establish the existence of the global classical solution to 1D/spherically symmetric compressible Navier-Stokes equations for isothermal flows with vacuum and large initial data.
This is a joint work with Guangyi Hong, Xiaofeng Hou and Hongyun Peng.
