Existence of Strong Solutions for Incompressible Magnetic Hydrodynamics

Abstract

We consider the existence of the local strong solutions of the zero Dirichlet problems of the coupled Navier-Stokes equations which govern the incompressible magnetic fluid in three dimensional bounded domain. We derive the local existence in time of a unique strong solution for boldmath u₀ belonging in IH^1/2. The proofs have been shown to apply the contraction mapping theorem by using the theory of the sub-differential operators.