On the inviscid limit of the Navier-Stokes equations

Constantin, Peter; Kukavica, Igor; Vicol, Vlad

doi:10.1090/S0002-9939-2015-12638-X

On the inviscid limit of the Navier-Stokes equations
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by Peter Constantin, Igor Kukavica and Vlad Vicol

Proc. Amer. Math. Soc. 143 (2015), 3075-3090

DOI: https://doi.org/10.1090/S0002-9939-2015-12638-X

Published electronically: March 4, 2015

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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.

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