On the rough solutions of 3D compressible Euler equations: an alternative proof

Abstract

The well-posedness of Cauchy problem of 3D compressible Euler equations is studied. By using Smith-Tataru's approach \cite{ST}, we prove the local existence, uniqueness and stability of solutions for Cauchy problem of 3D compressible Euler equations, where the initial data of velocity, density, specific vorticity $v, \rho \in H^s, \varpi \in H^{s_0} (2<s_0<s)$. It's an alternative and simplified proof of the result given by Q. Wang in \cite{WQEuler}.