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arXiv · 1808.03510

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

Shijin Ding·Zhilin Lin·Dongjuan Niu
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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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Shijin Ding, Zhilin Lin, Dongjuan Niu. 2018-08-10. Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations. https://doi.org/10.3934/dcds.2020193

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