Vorticity Leray- $$\alpha $$ model for Navier–Stokes equations with viscosity depending on the distance to the wall

Abstract

We introduce a vorticity Leray-\(\alpha \) model with eddy viscosity depending on \(d(x,\partial \Omega )^\eta \) where \(\partial \Omega \) is the boundary of the domain and \(\eta \in ]0;1[\). We prove that this system admits fairly regular weak solutions converging when \(\alpha \) goes to 0 to the solution of a reference system