Boundary Layers Associated with a Coupled Navier-Stokes/Allem-Cahn System: the Non-characteristic Boundary Case

Boundary Layers Associated with a Coupled Navier-Stokes/Allem-Cahn System: the Non-characteristic Boundary Case

Year:    2012

Author:    Xiaoqiang Xie

Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 66–78

Abstract

The goal of this article is to study the boundary layer of Navier-Stokes/Allen- Cahn system in a channel at small viscosity. We prove that there exists a boundary layer at the outlet (down-wind) of thickness n, where n is the kinematic viscosity. The convergence in L^2 of the solutions of the Navier-Stokes/Allen-Cahn equations to that of the Euler/Allen-Cahn equations at the vanishing viscosity was established. In two dimensional case we are able to derive the physically relevant uniform in space and time estimates, which is derived by the idea of better control on the tangential derivative and the use of an anisotropic Sobolve imbedding.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v25.n1.5

Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 66–78

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Boundary layers

Author Details

Xiaoqiang Xie

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