BOUNDARY LAYER FOR 3D PLANE PARALLEL CHANNEL FLOWS OF NONHOMOGENEOUS INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

摘要

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of nonho-mogeneous incompressible Navier-Stokes equations. The convergence is shown under various Sobolev norms, including the physically important space-time uniform norm, as well as the L~∞(H~1) norm. It is mentioned that the mathematical validity of the Prandtl boundary layer theory for nonlinear plane parallel flow is generalized to the nonhomogeneous case.