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arxiv: 1905.07851 · v1 · pith:NVDPALPP · submitted 2019-05-20 · math.AP

Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum

Huajun Gong , Jinkai Li , Xian-Gao Liu , Xiaotao Zhang This is my paper

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classification math.AP
keywords well-posednesscompressibleequationsnavier-stokesvacuuminitialisentropiclocal
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In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.

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