The Vacuum in Nonisentropic Gas Dynamics

TL;DR

This paper studies the conditions under which vacuum states occur in nonisentropic gas dynamics and introduces models that avoid vacuums, providing insights into the behavior of solutions in these systems.

Contribution

It characterizes when vacuums occur in nonisentropic gas dynamics and proposes models with unique solutions that do not develop vacuums.

Findings

Conditions for vacuum occurrence in solutions

Explicit criteria based on thermodynamic equations of state

Models with guaranteed vacuum-free solutions

Abstract

We investigate the vacuum in nonisentropic gas dynamics in one space variable, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem. We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.