The inviscid limit and boundary layers for navier-stokes flows

Yasunori Maekawa, Anna L. Mazzucato

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationHandbook of Mathematical Analysis in Mechanics of Viscous Fluids
PublisherSpringer International Publishing
Pages781-828
Number of pages48
ISBN (Electronic)9783319133447
ISBN (Print)9783319133430
DOIs
StatePublished - Apr 19 2018

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Inviscid Limit
Stokes flow
incompressible flow
Incompressible flow
Stokes Flow
Navier-Stokes
Boundary Layer
boundary layers
Boundary layers
Viscosity
viscosity
Vanishing Viscosity
Incompressible Viscous Flow
Inviscid Flow
applications of mathematics
fluid mechanics
Fluid Mechanics
Euler equations
Fluid mechanics
Incompressible Flow

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Engineering(all)

Cite this

Maekawa, Y., & Mazzucato, A. L. (2018). The inviscid limit and boundary layers for navier-stokes flows. In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (pp. 781-828). Springer International Publishing. https://doi.org/10.1007/978-3-319-13344-7_15
Maekawa, Yasunori ; Mazzucato, Anna L. / The inviscid limit and boundary layers for navier-stokes flows. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, 2018. pp. 781-828
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Maekawa, Y & Mazzucato, AL 2018, The inviscid limit and boundary layers for navier-stokes flows. in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, pp. 781-828. https://doi.org/10.1007/978-3-319-13344-7_15

The inviscid limit and boundary layers for navier-stokes flows. / Maekawa, Yasunori; Mazzucato, Anna L.

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, 2018. p. 781-828.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Maekawa Y, Mazzucato AL. The inviscid limit and boundary layers for navier-stokes flows. In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing. 2018. p. 781-828 https://doi.org/10.1007/978-3-319-13344-7_15