Asymptotic stability for the inflow problem of the heat-conductive ideal gas without viscosity

TL;DR

This paper investigates the stability of boundary layers and wave superpositions in a non-viscous ideal gas inflow problem, establishing existence and asymptotic stability of solutions using energy methods.

Contribution

It demonstrates the existence and stability of boundary layers and wave superpositions in a non-viscous ideal gas inflow problem, extending understanding of such flows.

Findings

Existence of boundary layers in different regions.

Global-in-time unique solutions established.

Asymptotic stability of boundary layers and wave superpositions.

Abstract

This paper is devoted to studying the inflow problem for an ideal polytropic model with non-viscous gas in one-dimensional half space. We showed the existence of the boundary layer in different areas. By employing the energy method, we also proved the unique global-in-time solution existed and the asymptotic stability of both the boundary layer and the superposition with the 3-rarefaction wave under some smallness conditions.