Steady and self similar full Euler flow

TL;DR

This paper investigates steady, self-similar solutions to the full two-dimensional Euler equations with a polytropic equation of state, establishing BV regularity under certain conditions and analyzing their structure.

Contribution

It proves BV regularity for entropy admissible steady solutions with non-vanishing velocity, density, and energy, and explores their structural properties.

Findings

Solutions are BV under specified conditions.

Entropy admissible solutions exhibit particular structural features.

Non-vanishing velocity, density, and energy are crucial assumptions.

Abstract

We consider solutions to the full (non-isentropic) two-dimensional Euler equations that are constant in time and along rays emanating from the origin. We prove that for a polytropic equation of state, entropy admissible solutions in $L^\infty$ with non-vanishing velocity, density, and internal energy must be $BV$. Moreover, we obtain some results concerning the structure of such solutions.