Singularities in Euler flows: multivalued solutions, shock waves, and phase transitions

TL;DR

This paper explores critical phenomena in 1D Euler gas flows, focusing on multivalued solutions, shock waves, and phase transitions, using geometric PDE methods to interpret singularities and solution behaviors.

Contribution

It introduces a geometric approach to analyze singularities, multivalued solutions, and phase transitions in Euler flows, providing new insights into their structure and propagation.

Findings

Multivalued solutions with singularities are characterized.

Shock wave fronts and phase transitions are analyzed.

Geometric PDE methods reveal solution structures and behaviors.

Abstract

In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from the geometrical theory of PDEs, in particular, symmetries and differential constraints to find solutions to the Euler system. Solutions obtained are multivalued, have singularities of projection to the plane of independent variables. We analyze the propagation of the shock wave front along with phase transitions.