The Validity Of Prandtl Boundary Layer Expansions For The Steady MHD Equations In Bounded Domains

In this paper,we consider the Prandtl boundary layer expansion for the incompressible viscous electrically conducting fluid with high Reynolds numbers in a domain with a moving flat boundary,which is governed by the following two dimensional steady incompressible viscous MHD equations in the domain ?:=[0,L]×[0,1]:The following boundary conditions are applied to the velocity field and magnetic field,respectively:(U^?,V^?)(X,0)=(u_b,0),((?)_YH^?,G^?)(X,0)=(0,0),Which ?:=(?)_XX+(?)_YY,(U^?,V^?)and (H^?,G^?) are velocity field and the magnetic field respectively,and P^? the pressure field is represented.? and ? is a positive constant.The purpose of this paper is to extend the[35]results to a more physically practical bounded domain.Assuming that the viscous and resistivity coefficients are of the same order of magnitude,the initial tangential magnetic field on the boundary does not degenerate.under the symmetry assumption,we demonstrate the validity of the plantl boundary layer expansion and estimate the error by multi-scale analysis.when the viscosity tends to zero,the convergence rate is given.The first Chapter introduces the research background and main results of boundary layer problem.The second Chapter of this paper is about constructing high-order approximate solutions.The third Chapter of this thesis is about estimating the remainder and proving the principal theorem 1.1.