### Abstract

We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.

Original language | English (US) |
---|---|

Pages (from-to) | 3075-3090 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 7 |

DOIs | |

State | Published - Jan 1 2015 |

### Fingerprint

### Keywords

- Boundary layer
- Euler equations
- Inviscid limit
- Navier-Stokes equations

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*143*(7), 3075-3090. https://doi.org/10.1090/S0002-9939-2015-12638-X

**On the inviscid limit of the navier-stokes equations.** / Constantin, Peter; Kukavica, Igor; Vicol, Vlad.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 143, no. 7, pp. 3075-3090. https://doi.org/10.1090/S0002-9939-2015-12638-X

}

TY - JOUR

T1 - On the inviscid limit of the navier-stokes equations

AU - Constantin, Peter

AU - Kukavica, Igor

AU - Vicol, Vlad

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.

AB - We consider the convergence in the L2 norm uniformly in time of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer then the inviscid limit holds.

KW - Boundary layer

KW - Euler equations

KW - Inviscid limit

KW - Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=84927726534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927726534&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2015-12638-X

DO - 10.1090/S0002-9939-2015-12638-X

M3 - Article

AN - SCOPUS:84927726534

VL - 143

SP - 3075

EP - 3090

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -