Global weak solutions to the density-dependent Hall-magnetohydrodynamics system
Analysis of PDEs
2021-09-01 v1
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.
Cite
@article{arxiv.2101.03775,
title = {Global weak solutions to the density-dependent Hall-magnetohydrodynamics system},
author = {Jin Tan},
journal= {arXiv preprint arXiv:2101.03775},
year = {2021}
}