Local-in-time well-posedness for compressible MHD boundary layer

Yongting Huang Cheng-Jie Liu Tong Yang

Fluid Dynamics and Shock Waves mathscidoc:1912.431014

Journal of Differential Equations, 266, (6), 2978-3013, 2019.3
In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work [27], we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.
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@inproceedings{yongting2019local-in-time,
  title={Local-in-time well-posedness for compressible MHD boundary layer},
  author={Yongting Huang, Cheng-Jie Liu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211226071928578},
  booktitle={Journal of Differential Equations},
  volume={266},
  number={6},
  pages={2978-3013},
  year={2019},
}
Yongting Huang, Cheng-Jie Liu, and Tong Yang. Local-in-time well-posedness for compressible MHD boundary layer. 2019. Vol. 266. In Journal of Differential Equations. pp.2978-3013. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211226071928578.
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