# PDE Seminar

## Local Well-posedness of non-isentropic Euler equations with physical vacuum

### 李亚纯 教授 (上海交通大学)

#### 2019年07月23日11:00-12:00 闵行校区数学楼102报告厅

Abstract:We consider the local well-posedness of the one-dimensional non-isentropic Euler equations with moving physical vacuum boundary. The physical vacuum singularity requires the sound speed to be scaled as the square root of the distance to the vacuum boundary. The main difficulty lies in the fact that the system of hyperbolic conservation laws becomes characteristic and degenerate at the vacuum boundary. To overcome this difficulty, our proof is based on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term. Then we construct solutions to this degenerate parabolic problem and establish uniform estimates that are independent of the artificial viscosity parameter. Solutions to the compressible Euler equations are obtained as the limit of the vanishing artificial viscosity. This is a joint work with Yongcai Geng, Dehua Wang and Runzhang Xu.