Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics

In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by free surface. An electromagnetic field generated some currents an external keeps MHD flow domain. On surface, boundary conditions for and transmission fields are imposed. We proved local well-posedness general setting domains from mathematical point view. The solutions obtained anisotropic space Hp1((0,T),Hq1)∩Lp((0,T),Hq3) velocity Hp1((0,T),Lq)∩Lp((0,T),Hq2) magnetic 2<p<∞, N<q<∞ 2/p+N/q<1. To prove our main result, used Lp-Lq maximal regularity theorem Stokes equations conditions, which have been Frolova second author.