Recent developments in mathematical aspects of relativistic fluids

Disconzi, Marcelo

doi:10.1007/s41114-024-00052-x

Title: Recent developments in mathematical aspects of relativistic fluids

Journal Article · 25 October 2024 · Living Reviews in Relativity

DOI: https://doi.org/10.1007/s41114-024-00052-x · OSTI ID:2473741

Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0024711

OSTI ID:: 2473741

Journal Information:: Living Reviews in Relativity, Journal Name: Living Reviews in Relativity Journal Issue: 1 Vol. 27; ISSN 1433-8351

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Country unknown/Code not available

Language:: English

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A Rigorous Formulation of the Cosmological Newtonian Limit Without Averaging Oliynyk, Todd A. Journal of Hyperbolic Differential Equations, Vol. 07, Issue 03 https://doi.org/10.1142/S0219891610002189	journal	September 2010
The global future stability of the FLRW solutions to the Dust-Einstein system with a positive cosmological constant Hadžić, Mahir; Speck, Jared Journal of Hyperbolic Differential Equations, Vol. 12, Issue 01 https://doi.org/10.1142/S0219891615500046	journal	March 2015
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The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy Luk, Jonathan; Speck, Jared Analysis & PDE, Vol. 17, Issue 3 https://doi.org/10.2140/apde.2024.17.831	journal	April 2024
Relativistic Shocks in viscous Gluon Matter Bouras, Ioannis Proceedings of XLVIII International Winter Meeting on Nuclear Physics in Memoriam of Ileana Iori — PoS(BORMIO2010) https://doi.org/10.22323/1.103.0010	conference	December 2010
Blowup of Small Data Solutions for a Quasilinear Wave Equation in Two Space Dimensions Alinhac, Serge The Annals of Mathematics, Vol. 149, Issue 1 https://doi.org/10.2307/121020	journal	January 1999
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Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics Disconzi, Marcelo M.; Shao, Yuanzhen Asymptotic Analysis https://doi.org/10.3233/ASY-241919	journal	July 2024
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New Developments in Relativistic Magnetohydrodynamics Hattori, Koichi; Hongo, Masaru; Huang, Xu-Guang Symmetry, Vol. 14, Issue 9 https://doi.org/10.3390/sym14091851	journal	September 2022
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On the existence of solutions and causality for relativistic viscous conformal fluids M. Disconzi, Marcelo Communications on Pure & Applied Analysis, Vol. 18, Issue 4 https://doi.org/10.3934/cpaa.2019075	journal	January 2019
Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics Bemfica, Fabio S.; Disconzi, Marcelo M.; Graber, P. Jameson Communications on Pure & Applied Analysis, Vol. 20, Issue 9 https://doi.org/10.3934/cpaa.2021068	journal	January 2021
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Local Hilbert expansion for the Boltzmann equation Guo, Yan; Jang, Juhi; Jiang, Ning Kinetic & Related Models, Vol. 2, Issue 1 https://doi.org/10.3934/krm.2009.2.205	journal	January 2009
A symmetrization of the relativistic Euler equations with several spatial variables G. LeFloch, Philippe; Ukai, Seiji Kinetic & Related Models, Vol. 2, Issue 2 https://doi.org/10.3934/krm.2009.2.275	journal	January 2009
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Rough solutions of the 3-D compressible Euler equations Wang, Qian Annals of Mathematics, Vol. 195, Issue 2 https://doi.org/10.4007/annals.2022.195.2.3	journal	March 2022
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