Existence of radially symmetric stationary solutions for viscous and Heat-conductive ideal Gas

TL;DR

This paper proves the existence and uniqueness of radially symmetric stationary solutions for viscous, heat-conductive ideal gases in exterior domains, including decay estimates near the far-field state.

Contribution

It establishes the unique existence of solutions for both inflow and outflow problems in exterior domains with decay rate estimates.

Findings

Unique existence of solutions near far-field state

Decay rate estimates towards far-field state

Applicability to both inflow and outflow boundary conditions

Abstract

We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are prescribed. The unique existence of the stationary solution is shown for both inflow and outflow problems in a suitably small neighborhood of the far-field state. Estimates of the algebraic decay rate toward the far field state are also obtained.