Speaker: 刘思乘博士，澳门大学

Title: Full compressible Euler equations in a physical vacuum

Language: Chinese

Time & Venue: 2025.11.26 13:00-14:00 腾讯会议：951-442-365

Abstract: This presentation addresses vacuum free-boundary problems for the non-isentropic compressible Euler equations, focusing on the dynamics of gases in the vicinity of vacuum boundaries, where the density approaches zero. The notion of a physical vacuum, with boundaries moving over time with finite non-zero normal accelerations, is of close relevance to the study of gaseous stars and shallow water waves. This talk primarily concentrates on the Hadamard-style local well-posedness of physical vacuum problems within suitable weighted Sobolev spaces. It will cover aspects such as existence, uniqueness, continuous dependence on initial data, a priori energy estimates, and continuation criteria. These results apply to low-regularity solutions, for which the velocity fields of free boundaries are only Lipschitz continuous, and the gas-vacuum interface is allowed to have unbounded curvature. This is the first well-posedness result for the full compressible Euler equations in a physical vacuum within multi-dimensional spaces. The approach is based on the framework of Eulerian coordinates. This talk is based on a joint work with Prof. Tao LUO at CityUHK.