TL;DR
This paper investigates singularities in one-dimensional Euler flows, introducing a new class of multivalued solutions for gas dynamics, and analyzes caustics and discontinuities in ideal gas models.
Contribution
It presents a novel approach using 2-forms on jet space to find multivalued solutions and study their singularities in gas dynamics.
Findings
Identified caustics in ideal gas flows.
Discovered discontinuity lines in the solution projections.
Developed a new class of multivalued solutions.
Abstract
In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a new class of multivalued solutions for an arbitrary thermodynamic state model and discuss singularities of their projections to the space of independent variables for the case of an ideal gas. Caustics and discontinuity lines are found.
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