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

Huajun Gong Shenzhen University Jinkai Li South China Normal University Xian-Gao Liu Fudan University Xiaotao Zhang South China Normal University

Analysis of PDEs mathscidoc:1905.03008

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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@inproceedings{huajunlocal,
  title={Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum},
  author={Huajun Gong, Jinkai Li, Xian-Gao Liu, and Xiaotao Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190520114429913609349},
}
Huajun Gong, Jinkai Li, Xian-Gao Liu, and Xiaotao Zhang. Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190520114429913609349.
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