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Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay

Cheng-Jie Liu Tong Yang

Analysis of PDEs mathscidoc:1912.43983

Journal de Mathmatiques Pures et Appliques, 108, (2), 150-162, 2017.8
Motivated by the paper Grard-Varet and Dormy (2010) [6] [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations in Sobolev spaces, this paper aims to extend the result in [6] to the case when the shear flow has general decay. The key observation is to construct an approximate solution that captures the initial layer to the linearized problem motivated by the precise formulation of solutions to the inviscid Prandtl equations.
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@inproceedings{cheng-jie2017ill-posedness,
  title={Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay},
  author={Cheng-Jie Liu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211042102525547},
  booktitle={Journal de Mathmatiques Pures et Appliques},
  volume={108},
  number={2},
  pages={150-162},
  year={2017},
}
Cheng-Jie Liu, and Tong Yang. Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay. 2017. Vol. 108. In Journal de Mathmatiques Pures et Appliques. pp.150-162. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211042102525547.
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