Unconditional stability of radially symmetric steady sates of compressible viscous fluids with inflow/outflow boundary conditions

TL;DR

This paper proves that specific radially symmetric steady states of compressible viscous fluids with inflow/outflow boundaries are unconditionally stable, ensuring convergence of solutions to these states regardless of initial conditions.

Contribution

It establishes the unconditional stability of radially symmetric steady states for compressible viscous fluids with inflow/outflow boundaries, a novel stability result.

Findings

Radially symmetric steady states are unconditionally stable.

Solutions converge to these steady states regardless of initial conditions.

The stability holds for the associated evolutionary problem.

Abstract

We show that certain radially symmetric steady states of compressible viscous fluids in domains with inflow/outflow boundary conditions are unconditionally stable. This means that any not necessarily radially symmetric solution of the associated evolutionary problem converges to a single radially symmetric steady state.