Inviscid Limit Problem of radially symmetric stationary solutions for compressible Navier-Stokes equation

TL;DR

This paper investigates the inviscid limit of radially symmetric stationary solutions for the compressible Navier-Stokes equations, demonstrating uniform convergence to Euler flows with algebraic rate estimates for both inflow and outflow problems.

Contribution

It establishes the inviscid limit behavior for radially symmetric solutions, including convergence results and rate estimates, for exterior problems in compressible fluid dynamics.

Findings

Uniform convergence of Navier-Stokes to Euler flow in outflow case.

Convergence to superposition of boundary layer and Euler flow in inflow case.

Algebraic rate estimates for the inviscid limit.

Abstract

The present paper is concerned with an inviscid limit problem of radially symmetric stationary solutions for an exterior problem in $\mathbb{R}^n (n\ge 2)$ to compressible Navier-Stokes equation, describing the motion of viscous barotropic gas without external forces, where boundary and far field data are prescribed. For both inflow and outflow problems, the inviscid limit is considered in a suitably small neighborhood of the far field state. For the outflow problem, we prove the uniform convergence of the Navier-Stokes flow toward the corresponding Euler flow in the inviscid limit. On the other hand, for the inflow problem, we show that the Navier-Stokes flow uniformly converges toward a linear superposition of the corresponding boundary layer profile and the Euler flow in the inviscid limit. The estimates of algebraic rate toward the inviscid limit are also obtained.