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We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system's noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid…

Mathematical Physics · Physics 2025-05-08 Keiichiro Takeda , Naoki Sato

Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…

Analysis of PDEs · Mathematics 2022-09-28 Theodore D. Drivas , Tarek M. Elgindi

Present investigation devoted to the dynamical study of Relativistic Hydrodynamics with some thermodynamical characteristics in $f(R,G)$ gravity towards spatially homogeneous isotropic cosmological model filled with isotropic fluid. We…

General Physics · Physics 2020-04-09 S. H. Shekh , Simran Arora , V. R. Chirde , P. K. Sahoo

This paper presents (Lagrangian) variational formulations for single and multicomponent semi-compressible fluids with both reversible (entropy-conserving) and irreversible (entropy-generating) processes. Semi-compressible fluids are useful…

Fluid Dynamics · Physics 2021-09-01 Christopher Eldred , François Gay-Balmaz

The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and…

Numerical Analysis · Mathematics 2025-09-01 Ferdinand Thein , Hendrik Ranocha

By refining the method proposed in arXiv:2010.07660, entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Noether conserved charge in the Einstein gravity…

General Relativity and Quantum Cosmology · Physics 2024-07-12 Shuichi Yokoyama

This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Eric Gourgoulhon

We develop a relativistic multifluid dynamics appropriate for describing neutron star cores at finite temperatures based on Carter's convective variational procedure. The model includes seven fluids, accounting for both normal and…

High Energy Astrophysical Phenomena · Physics 2020-09-14 Peter B. Rau , Ira Wasserman

We present a simple, analytic and straightforward method to elucidate the effects produced by polytropic fluids on any other gravitational source, no matter its nature, for static and spherically symmetric spacetimes. As a direct…

General Relativity and Quantum Cosmology · Physics 2022-03-30 J. Ovalle , E. Contreras , Z. Stuchlik

We consider a self-gravitating, rigidly rotating charged perfect fluid immersed in the Wald magnetosphere, constructed out of two linearly independent Killing vectors present in stationary and axially-symmetric spacetimes. We show that in…

General Relativity and Quantum Cosmology · Physics 2026-04-14 Paweł Doruchowski , Patryk Mach , Audrey Trova , Bakhtinur Juraev

We derive a priori error of the Godunov method for the multidimensional Euler system of gas dynamics. To this end we apply the relative energy principle and estimate the distance between the numerical solution and the strong solution. This…

Numerical Analysis · Mathematics 2021-11-12 Mária Lukáčová-Medviďová , Bangwei She , Yuhuan Yuan

This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In this third paper we elevate the Newtonian theory of the…

General Relativity and Quantum Cosmology · Physics 2024-06-06 Tom Cadogan , Eric Poisson

This article is a survey concerning the state-of-the-art mathematical theory of the Euler equations of incompressible homogenous ideal fluid. Emphasis is put on the different types of emerging instability, and how they may be related to the…

Analysis of PDEs · Mathematics 2015-06-26 Claude Bardos , Edriss S. Titi

In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…

Analysis of PDEs · Mathematics 2026-04-02 Talita Mello , Wladimir Neves

In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not…

Numerical Analysis · Mathematics 2019-07-09 Andrew R. Winters , Christof Czernik , Moritz B. Schily , Gregor J. Gassner

The present work concerns the derivation of a fully well-balanced Godunov-type finite volume scheme for the Euler equations with a gravitational potential based on an approximate Riemann solver in a one-dimensional framework. It is an…

Numerical Analysis · Mathematics 2025-10-08 Victor Michel-Dansac , Andrea Thomann

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.

General Relativity and Quantum Cosmology · Physics 2009-07-24 Nikodem J. Poplawski

Flow past a line vortex in a simple perfect fluid or superfluid gives rise to a transverse Magnus force that is given by the well known Joukowski lift formula. The problem of generalising this to multiconstituent superfluid models has been…

Condensed Matter · Physics 2007-05-23 Brandon Carter , David Langlois , Reinhard Prix

Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…

Analysis of PDEs · Mathematics 2007-11-06 Philippe G. LeFloch

A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a…

Fluid Dynamics · Physics 2015-05-14 Bhimsen K. Shivamoggi