Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations

Abstract

We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a strong compactness argument to justify the inviscid limit. Our approach does not rely on the justification of asymptotic expansions. In particular, we get a new existence result for the Euler equations with free surface from the one for Navier-Stokes.

References in corpus (2)

• A note on the Prandtl boundary layers
• Decay of viscous surface waves without surface tension

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