Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data

Jinkai Li South China Normal University Mingjie Li Minzu University of China

Analysis of PDEs mathscidoc:2108.03006

2021.7
In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of the proof is to establish the a priori estimates on the effective viscous flux and a newly introduced ``transverse effective viscous flux" vector field inducted by the transverse magnetic field. The initial density is assumed only to be uniformly bounded and of finite mass and, in particular, the vacuum and discontinuities of the density are allowed.
compressible magnetohydrodynamic equations; global strong solution; vacuum; large initial data; effective viscous flux; transverse effective viscous flux.
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@inproceedings{jinkai2021global,
  title={Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data},
  author={Jinkai Li, and Mingjie Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210824233040761251870},
  year={2021},
}
Jinkai Li, and Mingjie Li. Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210824233040761251870.
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