arXiv:1610.05372 Abstract | arXiv Analytics

arXiv:1610.05372 [math.AP]Abstract References Reviews Resources

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

Published 2016-10-17Version 1

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.

Comments: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.com

Categories: math.AP

Subjects: 76D10, 35Q30, 35Q31

Keywords: boundary layer, inviscid limit, navier-stokes flows, modeling inviscid incompressible flows, viscous incompressible flows converge

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