### 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) |
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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 | |

State | Published - Apr 19 2018 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*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

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*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.

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

TY - CHAP

T1 - The inviscid limit and boundary layers for navier-stokes flows

AU - Maekawa, Yasunori

AU - Mazzucato, Anna L.

PY - 2018/4/19

Y1 - 2018/4/19

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85054357474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054357474&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-13344-7_15

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

M3 - Chapter

AN - SCOPUS:85054357474

SN - 9783319133430

SP - 781

EP - 828

BT - Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

PB - Springer International Publishing

ER -