Uniform regularity for the Navier-Stokes equation with Navier boundary condition

Abstract

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 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 $L^{\infty }$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

Cited by in corpus (9)

• Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition
• The inviscid limit of Navier-Stokes for analytic data on the half-space
• Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions
• Smooth controllability of the Navier-Stokes equation with Navier conditions. Application to Lagrangian controllability
• Global Solutions to an initial boundary problem for the compressible 3-D MHD equations with Navier-slip and perfectly conducting boundary conditions in exterior domains
• Uniform Regularity and Vanishing Viscosity limit for the chemotaxis-Navier-Stokes system in a 3D bounded domain
• Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array
• Vanishing viscosity limits for axisymmetric flows with boundary
• On the "viscous incompressible fluid + rigid body" system with Navier conditions