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}.

arXiv comment62 pages. Welcome all comments. arXiv admin note: text overlap with arXiv:2012.01060

References in corpus (3)

• Strong illposedness of the incompressible Euler equation in integer $C^m$ spaces
• A priori estimates for the free-boundary 3-D compressible Euler equations in physical vacuum
• Rough sound waves in $3D$ compressible Euler flow with vorticity

Cited by in corpus (2)

• Rough sound waves in $3D$ compressible Euler flow with vorticity
• Low regularity ill-posedness and shock formation for 3D ideal compressible MHD