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

Nader Masmoudi (1) , Frédéric Rousset (2, 3)

1 CIMS - Courant Institute of Mathematical Sciences [New York]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Equations aux dérivées partielles [math.AP]

Nader Masmoudi, Frédéric Rousset. Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 2017, 223 (1), pp.301-417. ⟨10.1007/s00205-016-1036-5⟩. ⟨hal-00707831⟩