On Vanishing Viscosity with Inflow, Outflow

TL;DR

This paper proves that solutions of the Navier-Stokes equations with inflow and outflow boundary conditions converge to Euler solutions as viscosity approaches zero, extending previous methods to include nonzero tangential outflow components.

Contribution

It extends the convergence analysis of Navier-Stokes to Euler equations to cases with nonzero tangential outflow, broadening the understanding of boundary condition effects.

Findings

Established convergence of Navier-Stokes solutions to Euler solutions with inflow/outflow boundaries

Extended previous methods to handle nonzero tangential outflow components

Provided mathematical proof under specified boundary conditions

Abstract

We establish convergence as the viscosity vanishes of solutions of the Navier-Stokes equations to a solution of the Euler equations for inflow, outflow boundary conditions. We extend the approach of Temam and Wang 2002, allowing the tangential component on outflow to be nonzero.