Physical Vacuum Problems for the Full Compressible Euler Equations: Low-regularity Hadamard-style Local Well-posedness

Abstract

This manuscript concerns the dynamics of non-isentropic compressible Euler equations in a physical vacuum. We establish the Hadamard-style local well-posedness in low-regularity weighted Sobolev spaces, where the gas-vacuum interface is allowed to have unbounded curvature, demonstrating existence, uniqueness, and continuous dependence on initial data. Additionally, we prove sharp a priori energy estimates and continuation criteria. The approach is based on the framework of Eulerian coordinates, avoiding the regularity issues of the flow map and the high nonlinearity induced by the Lagrangian transformation.