Stationary flows for viscous heat-conductive fluid in a perturbed half-space

TL;DR

This paper proves the existence and stability of multidirectional stationary flows for a viscous, heat-conductive compressible fluid in a perturbed half-space, extending understanding of such flows under outflow and supersonic conditions.

Contribution

It establishes the unique existence and asymptotic stability of multidirectional stationary solutions for the non-isentropic compressible Navier-Stokes equations in a perturbed half-space.

Findings

Unique stationary solutions exist under outflow and supersonic conditions.

Stationary solutions depend on all spatial directions and exhibit multidirectional flow.

Asymptotic stability of these solutions is proven.

Abstract

We consider the non-isentropic compressible Navier-Stokes equation in a perturbed half space with an outflow boundary condition as well as the supersonic condition. This equation models a compressible viscous, heat-conductive, and Newtonian polytropic fluid. We show the unique existence of stationary solutions for the perturbed half-space. The stationary solution constructed in this paper depends on all directions and has multidirectional flow. We also prove the asymptotic stability of this stationary solution.