Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in 3D

Kefeng Liu Yuan Yuan

Analysis of PDEs mathscidoc:1912.43125

arXiv preprint arXiv:1802.00127, 2018.2
In this paper we establish the local-in-time existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in three-dimensional space. The vanishing density and temperature condition is imposed on the free boundary, which captures the motions of the non-isentropic viscous gas surrounded by vacuum with bounded entropy. We also assume some proper decay rates of the density towards the boundary and singularities of derivatives of the temperature across the boundary on the initial data, which coincides with the physical vacuum condition for the isentropic flows. This extends the previous result of Liu [arXiv: 1612.07936] by removing the spherically symmetric assumption and considering more general initial density and temperature profiles.
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@inproceedings{kefeng2018local,
  title={Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in 3D},
  author={Kefeng Liu, and Yuan Yuan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111703761797685},
  booktitle={arXiv preprint arXiv:1802.00127},
  year={2018},
}
Kefeng Liu, and Yuan Yuan. Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes equations in 3D. 2018. In arXiv preprint arXiv:1802.00127. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111703761797685.
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