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Article

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

1
V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, Russia
2
Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia
*
Author to whom correspondence should be addressed.
Symmetry 2021, 13(1), 54; https://doi.org/10.3390/sym13010054
Received: 28 November 2020 / Revised: 29 December 2020 / Accepted: 30 December 2020 / Published: 31 December 2020
(This article belongs to the Special Issue Geometric Analysis of Nonlinear Partial Differential Equations)
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 partial differential equations (PDEs), in particular symmetries and differential constraints, to find solutions to the Euler system. Solutions obtained are multivalued and have singularities of projection to the plane of independent variables. We analyze the propagation of the shockwave front along with phase transitions. View Full-Text
Keywords: Euler equations; shockwaves; phase transitions; symmetries Euler equations; shockwaves; phase transitions; symmetries
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MDPI and ACS Style

Lychagin, V.; Roop, M. Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions. Symmetry 2021, 13, 54. https://doi.org/10.3390/sym13010054

AMA Style

Lychagin V, Roop M. Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions. Symmetry. 2021; 13(1):54. https://doi.org/10.3390/sym13010054

Chicago/Turabian Style

Lychagin, Valentin, and Mikhail Roop. 2021. "Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions" Symmetry 13, no. 1: 54. https://doi.org/10.3390/sym13010054

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