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

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