Uniform regularity and vanishing viscosity limit for the incompressible non-resistive MHD system with transverse magnetic field

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.