Euler Equations with Physical Vacuum Boundary

Juhi Jang
Institute for Advanced Study

Abstract: We study one-dimensional compressible Euler equations arising in gas dynamics when the vacuum is allowed initially. It is considered as a vacuum free boundary problem. The difficulty lies in the fact that the system becomes degenerate along the vacuum boundary. Some local existence result, where initial vacuum state is rather regular, is reviewed. We present new a priori estimates for the physical vacuum boundary in Lagrangian coordinates.