Validity of boundary layer theory for the 3D plane‐parallel nonhomogeneous electrically conducting flows

Abstract

In this paper, we validate the boundary layer expansion for a family of plane‐parallel flows to nonhomogeneous incompressible magnetohydrodynamic equations with no‐slip boundary conditions imposed on velocity field and perfectly conducting conditions on magnetic field. The convergence rate is established in Sobolev sense. We extend the result of Navier–Stokes system to the case of MHD equations and also investigate the stabilizing effect of the magnetic field by considering the uniform magnetic field.