On the inviscid limit of the Navier-Stokes equations

Peter Constantin; Igor Kukavica; Vlad Vicol

On the inviscid limit of the Navier-Stokes equations

Analysis of PDEs 2014-04-01 v2

Authors: Peter Constantin , Igor Kukavica , Vlad Vicol

Abstract

We consider the convergence in the $L^2$ 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.

Keywords

Navier-Stokes equations Euler equations inviscid limit Dirichlet boundary conditions slip boundary conditions Oleinik conditions Kato-like boundary layer vorticity

Cite

@article{arxiv.1403.5748,
  title  = {On the inviscid limit of the Navier-Stokes equations},
  author = {Peter Constantin and Igor Kukavica and Vlad Vicol},
  journal= {arXiv preprint arXiv:1403.5748},
  year   = {2014}
}

Comments

Improved the main result and fixed a number of typos

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