On the inviscid limit of the Navier-Stokes equations

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.

arXiv commentImproved the main result and fixed a number of typos

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Cited by in corpus (2)

• Almost global existence for the Prandtl boundary layer equations
• Observations on the vanishing viscosity limit