Global Strong Solutions of the Density Dependent Incompressible MHD System with Zero Resistivity in a Bounded Domain

摘要

In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u(0) and b(0) satisfy that (d - 2)parallel to del u(0)parallel to(L)2 + parallel to b(0)parallel to w(1,p) are sufficiently small with d p 2d/d-2 (d = 2, 3). We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Omega.