# PDE Seminar

## Global existence of finite energy weak solution to the Compressible Euler Equations with spherical Symmetry and Large Initial Data

### 王勇 (中科院数学与系统科学研究院)

#### 2019年07月13日11:00-12:00 闵行校区数学楼102报告厅

Abstract: For far field density $\bar{\rho}>0$, various evidences indicate that the spherically symmetric solutions of the compressible Euler equations may blow up near the origin at certain time. In this paper, we established the global existence of finite energy weak solution by vanishing viscosity limit of weak solutions of the compressible Navier-Stokes equations with spherical symmetry and large initial data in $\mathbb{R}^N (N\geq2)$ and $\bar{\rho}>0$. This indicates that concentration is not formed in the vanishing physical viscosity limit, even though the density may blow up at certain time.