Asymptotic stability of the rarefaction wave for the non-viscous and heat-conductive ideal gas in half space

TL;DR

This paper proves the asymptotic stability of the 3-rarefaction wave for a non-viscous, heat-conductive ideal gas in a half-space, using an elementary energy method to handle boundary effects.

Contribution

It demonstrates the stability of the 3-rarefaction wave in a non-viscous, heat-conductive gas model, addressing boundary challenges with a novel elementary energy approach.

Findings

3-rarefaction wave is stable under smallness conditions

Boundary terms are effectively controlled despite low dissipativity

Elementary energy method is successfully applied

Abstract

This paper is concerned with the impermeable wall problem for an ideal polytropic model of non-viscous and heat-conductive gas in one-dimensional half space. It is shown that the 3-rarefaction wave is stable under some smallness conditions. The proof is given by an elementary energy method and the key point is to control the boundary terms due to the less dissipativity of the system.