The inviscid limit and boundary layers for navier-stokes flows

Yasunori Maekawa; Anna Mazzucato

doi:10.1007/978-3-319-13344-7_15

The inviscid limit and boundary layers for navier-stokes flows

Yasunori Maekawa, Anna Mazzucato

Research output: Chapter in Book/Report/Conference proceeding › Chapter

20 Scopus citations

Abstract

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 chapter is to review recent progress on the mathematical analysis of this problem in each category.

Original language	English (US)
Title of host publication	Handbook of Mathematical Analysis in Mechanics of Viscous Fluids
Publisher	Springer International Publishing
Pages	781-828
Number of pages	48
ISBN (Electronic)	9783319133447
ISBN (Print)	9783319133430
DOIs	https://doi.org/10.1007/978-3-319-13344-7_15
State	Published - Apr 19 2018

All Science Journal Classification (ASJC) codes

General Mathematics
General Physics and Astronomy
General Engineering

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10.1007/978-3-319-13344-7_15

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AB - 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 chapter is to review recent progress on the mathematical analysis of this problem in each category.

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The inviscid limit and boundary layers for navier-stokes flows

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