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arXiv · 2101.03775

Global weak solutions to the density-dependent Hall-magnetohydrodynamics system

Jin Tan
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Abstract

We are concerned with the global existence of finite energy weak solutions to 3D density-dependent magnetohydrodynamics (MHD) system with Hall-effect set in a general smooth bounded domain. The perfectly conducting wall boundary condition is imposed on the magnetic field. Due to the degeneracy of Hall-effect term (a tri-linear term) in vacuum, we assumed initial density lies in the bounded function space and having a positive lower bound. Particularly, these bounds are preserved by the density transport equation which helps yield a satisfying compactness argument of the magnetic field.

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Jin Tan. 2021-01-11. Global weak solutions to the density-dependent Hall-magnetohydrodynamics system. https://doi.org/10.1007/s00021-021-00613-y

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