Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations

Abstract

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flow of nonhomogeneous incompressible Navier-Stokes equations. The convergence for the density and velocity are shown under various Sobolev norms, including the physically important space-time uniform norm, as well as the $L^{\infty }(H^1)$ 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.

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