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On the rough solutions of 3D compressible Euler equations: an alternative proof (2104.12299v2)
Published 26 Apr 2021 in math.AP
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 $v, \rho \in Hs, \varpi \in H{s_0} (2<s_0<s)$. It's an alternative and simplified proof of the result given by Q. Wang in \cite{WQEuler}.
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