On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions

Abstract

. The vanishing viscosity limit is considered for the incompressible 2D NavierStokes equations in a bounded domain. Motivated by studies of turbulent flow we suppose Navier's friction condition in the tangential direction, i.e. creation of a vorticity proportional to the tangential velocity. We prove existence of the regular solutions for the Navier-Stokes equations with smooth compatible data and of the solutions with bounded vorticity for initial vorticity being only bounded. Finally, we establish a uniform L 1 -bound for the vorticity and convergence to the incompressible 2D Euler equations in the inviscid limit. 1. Introduction The investigation of the inviscid limit of solutions of the Navier-Stokes equations is a classical issue. Some studies handle the case where the fluid domain has no boundary (the whole space or periodic geometry) , see for example Constantin, Foias [4] and Constantin, Wu [5]. In such cases, we are rid of the particular difficulties caused by the classical ...