Remarks about the inviscid limit for the nn-dimension magnetohydrodynamic system in the LpLp type space

In this paper, we prove that as the viscosity and resistivity go to zero, the solution of the Cauchy problem for the homogeneous incompressible MHD system converges to the solution of the ideal MHD system in the LpLp type space. The convergence rate is also obtained simultaneously. To the author’s knowledge, this is the first instance in which considering the inviscid and non-resistive limit for MHD system in the Lp(p≠2) type space.