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

TL;DR

This paper studies the behavior of 3D incompressible Navier-Stokes solutions as viscosity approaches zero, under generalized slip boundary conditions, providing uniform convergence estimates to Euler solutions.

Contribution

It establishes uniform convergence rates for Navier-Stokes solutions to Euler solutions with generalized slip boundary conditions in a bounded domain.

Findings

Derived uniform estimates on convergence rates in L^2 and H^1 norms.

Proved vanishing viscosity limit under 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 (\ref{VSg}). Some uniform estimates on rates of convergence in $C([0,T],L^2(\Omega))$ and $C([0,T],H^1(\Omega))$ of the solutions to the corresponding solutions of the idea Euler equations with the standard slip boundary condition are obtained.