Boundary layer for 3D nonlinear parallel pipe flow of nonhomogeneous incompressible Navier-Stokes equations

摘要

In this paper, we justify the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear parallel pipe flow of nonhomogeneous incompressible Navier-Stokes equations. The convergence for velocity is shown under various Sobolev norms. In addition, the higher-order asymptotic expansions are also considered. And the mathematical validity of the Prandtl boundary layer theory for nonlinear parallel pipe flow is generalized to the nonhomogeneous case.