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Compressible Euler equations with vacuum

Tai-Ping Liu Tong Yang

Analysis of PDEs mathscidoc:1912.43930

Journal of differential equations, 140, (2), 223-237, 1997.11
In this paper, we first show that the regular solutions of compressible Euler equations in<i>R</i><sup>3</sup>with damping will not be global if the initial density function has compact support. This implies that<i>c</i><sup>2</sup>cannot be smooth across the boundary<i></i>separating the gas and the vacuum after a finite time, where<i>c</i>is the speed of sound. Then we study the local existence of solutions for isentropic gas flow in<i>R</i>when<i>c<sup></sup></i>, 0&lt;<i></i>1, is smooth across<i></i>, using the energy method and the characteristics method.
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@inproceedings{tai-ping1997compressible,
  title={Compressible Euler equations with vacuum},
  author={Tai-Ping Liu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210727370796494},
  booktitle={Journal of differential equations},
  volume={140},
  number={2},
  pages={223-237},
  year={1997},
}
Tai-Ping Liu, and Tong Yang. Compressible Euler equations with vacuum. 1997. Vol. 140. In Journal of differential equations. pp.223-237. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210727370796494.
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