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Local existence with physical vacuum boundary condition to Euler equations with damping

Chao-Jiang Xu Tong Yang

Analysis of PDEs mathscidoc:1912.43954

Journal of Differential Equations, 210, (1), 217-231, 2005.3
In this paper, we consider the local existence of solutions to Euler equations with linear damping under the assumption of physical vacuum boundary condition. By using the transformation introduced in Lin and Yang (Methods Appl. Anal. 7 (3) (2000) 495) to capture the singularity of the boundary, we prove a local existence theorem on a perturbation of a planar wave solution by using LittlewoodPaley theory and justifies the transformation introduced in Liu and Yang (2000) in a rigorous setting.
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@inproceedings{chao-jiang2005local,
  title={Local existence with physical vacuum boundary condition to Euler equations with damping},
  author={Chao-Jiang Xu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210901713939518},
  booktitle={Journal of Differential Equations},
  volume={210},
  number={1},
  pages={217-231},
  year={2005},
}
Chao-Jiang Xu, and Tong Yang. Local existence with physical vacuum boundary condition to Euler equations with damping. 2005. Vol. 210. In Journal of Differential Equations. pp.217-231. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210901713939518.
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