On the inviscid limit of the 2D Magnetohydrodynamic system with vorticity in Yudovich-type space

摘要

In this paper, we first prove the existence and uniqueness of solutions only with magnetic diffusion for the vorticity being Yudovich-type space, by establishing some new time weighted estimates of the magnetic field, which improves the corresponding results of C. Cao, J. Wu and B. Yuan [5], and of Q. Jiu and J. Zhao [16]. Furthermore, we prove a global result on the inviscid limit of the two-dimensional Magnetohydrodynamic equations with data belonging to the Yudovich type.