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

摘要

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, ntimes(omega^{varepsilon}) = [B u^{varepsilon}]_{tau} {rm on} partialvarOmega). 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.