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.

Keywords

Navier–Stokes equations / Slip boundary conditions / Inviscid limit