Well-posedness for rough solutions of the 3D compressible Euler equations

Abstract

In this paper we prove full local well-posedness for the Cauchy problem for the compressible 3D Euler equation, i.e. local existence, uniqueness, and continuous dependence on initial data, with initial velocity, density and vorticity $({\mathbf{v}}_0,{\rho }_0,{\mathbf{w}}_0)\in H^{2+}\times H^{2+}\times H^2$, improving on the regularity conditions of \cite{WQEuler}. The continuous dependence on initial data for rough solutions of the compressible Euler system is new, even with the same regularity conditions as in \cite{WQEuler}. In addition, we prove new local well-posedness results for the 3D compressible Euler system with entropy.

arXiv commentWelcome all comments. This preprint covers our former one arXiv:2104.12299