Open AccessWell-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity
Author(s) -
Weixi Li,
Rui Xu
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021082
Subject(s) - sobolev space , uniqueness , magnetohydrodynamics , viscosity , mathematics , boundary layer , mathematical analysis , boundary (topology) , boundary value problem , physics , magnetic field , mechanics , thermodynamics , quantum mechanics
We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields dominates. This gives a complement to the previous works of Liu-Xie-Yang [Comm. Pure Appl. Math. 72 (2019)] and Liu-Wang-Xie-Yang [J. Funct. Anal. 279 (2020)], where the well-posedness theory was established for the MHD boundary layer systems with both viscosity and resistivity and with viscosity only, respectively. We use the pseudo-differential calculation, to overcome a new difficulty arising from the treatment of boundary integrals due to the absence of the diffusion property for the velocity.