On the Inviscid Limit of the 3D Navier–Stokes Equations with Generalized Navier-Slip Boundary Conditions

Abstract

In this paper, we investigate the vanishing viscosity limit problem for the 3-dimensional (3D) incompressible Navier–Stokes equations in a general bounded smooth domain of R 3 with the generalized Navier-slip boundary conditions \(u^{\varepsilon}\cdot n = 0,\ n\times(\omega^{\varepsilon}) = [B u^{\varepsilon}]_{\tau}\ {\rm on} \ \partial\varOmega\). Some uniform estimates on rates of convergence in C([0,T],L 2(Ω)) and C([0,T],H 1(Ω)) of the solutions to the corresponding solutions of the ideal Euler equations with the standard slip boundary condition are obtained.