Uniform regularity and vanishing viscosity limit for the incompressible non-resistive MHD system with TMF
Cheng‐Jie Liu, Feng Xie, Tong Yang
Abstract
<p style="text-indent:20px;">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 <inline-formula><tex-math id="M1">\begin{document}$ L^\infty $\end{document}</tex-math></inline-formula> norm in a fixed time interval independent of the viscosity coefficient. As a direct consequence, the inviscid limit from the viscous MHD system to the ideal MHD system is established in <inline-formula><tex-math id="M2">\begin{document}$ L^\infty $\end{document}</tex-math></inline-formula>-norm. In addition, the analysis shows that the boundary layer effect is weak because of the transverse magnetic field.