Uniform Regularity for the Navier-Stokes Equation with Navier Boundary Condition

Nader Masmoudi , Frédéric Rousset (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L (a). This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

Mots clés: incompressible limit; initial data; layers; stability; system; existence; domain; Vanishing viscosity limit; rotating fluids; Euler equations

Domaines: Equations aux dérivées partielles [math.AP]

Nader Masmoudi, Frédéric Rousset. Uniform Regularity for the Navier-Stokes Equation with Navier Boundary Condition. Archive for Rational Mechanics and Analysis, 2012, 203 (2), pp.529-575. ⟨10.1007/s00205-011-0456-5⟩. ⟨hal-00673262⟩