Open AccessUniform regularity and vanishing viscosity limit for the incompressible non-resistive MHD system with TMF
Author(s) -
Chengjie Liu,
Feng Xie,
Tong Yang
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021073
Subject(s) - magnetohydrodynamics , sobolev space , inviscid flow , physics , norm (philosophy) , bounded function , magnetic field , compressibility , mathematical analysis , mathematics , classical mechanics , mechanics , quantum mechanics , political science , law
This paper is concerned with the vanishing viscosity limit for the incompressible MHD system without magnetic diffusion effect in the half space under the influence of a transverse magnetic field on the boundary. We prove that the solution to the incompressible MHD system is uniformly bounded in both conormal Sobolev norm and \begin{document}$ L^\infty $\end{document} norm in a fixed time interval independent of the viscosity coefficient. As a direct consequence, the inviscid limit from the viscous MHD system to the ideal MHD system is established in \begin{document}$ L^\infty $\end{document} -norm. In addition, the analysis shows that the boundary layer effect is weak because of the transverse magnetic field.