Abstract
Relativistic Navier-Stokes equations express the conservation of the energy-momentum tensor and the particle number current in terms of the local hydrodynamic variables: temperature, fluid velocity, and the chemical potential. We show that the viscous-fluid equations are stable and causal if one adopts suitable non-equilibrium definitions of the hydrodynamic variables.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.D. Landau and E.M. Lifshitz, Fluid mechanics, Pergamon, U.K. (1987).
C. Eckart, The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid, Phys. Rev. 58 (1940) 919 [INSPIRE].
W.A. Hiscock and L. Lindblom, Generic instabilities in first-order dissipative relativistic fluid theories, Phys. Rev. D 31 (1985) 725 [INSPIRE].
W.A. Hiscock and L. Lindblom, Linear plane waves in dissipative relativistic fluids, Phys. Rev. D 35 (1987) 3723 [INSPIRE].
P. Romatschke and U. Romatschke, Relativistic fluid dynamics in and out of equilibrium, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (2019) [arXiv:1712.05815] [INSPIRE].
C. Gale, S. Jeon and B. Schenke, Hydrodynamic modeling of heavy-ion collisions, Int. J. Mod. Phys. A 28 (2013) 1340011 [arXiv:1301.5893] [INSPIRE].
S. Jeon and U. Heinz, Introduction to hydrodynamics, Int. J. Mod. Phys. E 24 (2015) 1530010 [arXiv:1503.03931] [INSPIRE].
P. Kovtun, First-order relativistic hydrodynamics is stable, JHEP 10 (2019) 034 [arXiv:1907.08191] [INSPIRE].
F.S. Bemfica, M.M. Disconzi and J. Noronha, Causality and existence of solutions of relativistic viscous fluid dynamics with gravity, Phys. Rev. D 98 (2018) 104064 [arXiv:1708.06255] [INSPIRE].
F.S. Bemfica, M.M. Disconzi and J. Noronha, Nonlinear causality of general first-order relativistic viscous hydrodynamics, Phys. Rev. D 100 (2019) 104020 [arXiv:1907.12695] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
R. Fox, C.G. Kuper and S.G. Lipson, Faster-than-light group velocities and causality violation, Proc. Roy. Soc. Lond. A 316 (1970) 515.
G.A. Korn and T.M. Korn, Mathematical handbook for scientists and engineers: definitions, theorems, and formulas for reference and review, McGraw-Hill, U.S.A. (1968).
R. Courant and D. Hilbert, Methods of mathematical physics II. Partial differential equations, Wiley, U.S.A. (1989).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.04102
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Hoult, R.E., Kovtun, P. Stable and causal relativistic Navier-Stokes equations. J. High Energ. Phys. 2020, 67 (2020). https://doi.org/10.1007/JHEP06(2020)067
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2020)067