Inviscid Limit of 3D Nonhomogeneous Navier–Stokes Equations with Slip Boundary Conditions

Abstract

In this paper, we consider the inviscid limit of a nonhomogeneous incompressible Navier–Stokes system with a slip-without-friction boundary condition. We study the convergence in strong norms for a solution and obtain the convergence rate in space W2,p(Ω) when the boundary is flat. We need to establish the uniform bound of the solution in space W3,p(Ω), and the key of proofs is to obtain a priori estimation of ∂tu in space W1,p(Ω).