Local Well-posedness for the Magnetohydrodynamics in the different two liquids case

Abstract

We prove the local well-posedness for a two phase problem of magnetohydrodynamics with a sharp interface. The solution is obtained in the maximal regularity space: $H_p^1((0,T),L_q)\cap L_p((0,T),H_q^2)$ with $1<p,q<\infty$ and 2/p + N/q < 1$,where$N$ is the space dimension