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The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of…

Numerical Analysis · Mathematics 2020-02-05 Matthias Kunik , Hailiang Liu , Gerald Warnecke

Fluid dynamic limit to compressible Euler equations from compressible Navier-Stokes equations and Boltzmann equation has been an active topic with limited success so far. In this paper, we consider the case when the solution of the Euler…

Analysis of PDEs · Mathematics 2010-11-10 Feimin Huang , Yi Wang , Tong Yang

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This systems it is a simplification of a recently propose system of five conservations laws by Bouchut and Boyaval that model…

Analysis of PDEs · Mathematics 2016-11-15 Richard De la cruz , Juan C. Juajibioy , Juan Galvis , Leonardo Rendón

We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the…

Mathematical Physics · Physics 2014-11-18 Patryk Mach , Malgorzata Pietka

Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…

Analysis of PDEs · Mathematics 2026-05-27 Elisabetta Chiodaroli , Eduard Feireisl , Ondřej Kreml , Simon Markfelder

We study the stochastically forced system of isentropic Euler equations of gas dynamics with a $\gamma$-law for the pressure. We show the existence of martingale weak entropy solutions; we also discuss the existence and characterization of…

Analysis of PDEs · Mathematics 2015-12-18 Florent Berthelin , Julien Vovelle

We solve the Riemann problem for the deceleration of an arbitrarily magnetized relativistic flow injected into a static unmagnetized medium in one dimension. We find that for the same initial Lorentz factor, the reverse shock becomes…

We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the…

Analysis of PDEs · Mathematics 2019-01-30 Shuyang Xiang , Yangyang Cao

We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…

General Relativity and Quantum Cosmology · Physics 2019-04-08 Christopher S. Gallagher , Timothy Clifton

A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically…

Plasma Physics · Physics 2017-11-22 Peifeng Fan , Hong Qin , Jian Liu , Nong Xiang , Zhi Yu

In this short note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove nonuniqueness of admissible weak solutions that start…

Analysis of PDEs · Mathematics 2017-07-04 Jan Březina , Elisabetta Chiodaroli , Ondřej Kreml

In this paper on hyperbolic systems of conservation laws in one space dimension, we give a complete picture of stability for all solutions to the Riemann problem which contain only extremal shocks. We study stability of the Riemann problem…

Analysis of PDEs · Mathematics 2021-03-02 Sam G. Krupa

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

We construct centered rarefaction wave solutions given background solutions to the compressible Euler equations. The flow considered in this article is the homentropic flow of perfect gas governed by compressible Euler equations and the…

Analysis of PDEs · Mathematics 2025-12-02 Ruotong Zhang

In this paper we extend and complement some recent results by Chiodaroli, De Lellis and Kreml on the well-posedness issue for weak solutions of the compressible isentropic Euler system in $2$ space dimensions with pressure law…

Analysis of PDEs · Mathematics 2014-08-26 Elisabetta Chiodaroli , Ondřej Kreml

We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…

Analysis of PDEs · Mathematics 2016-03-16 Nina Aguillon

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…

Statistical Mechanics · Physics 2022-01-12 Takashi Arima , Maria Cristina Carrisi , Sebastiano Pennisi , Tommaso Ruggeri

We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely the 3D radiative compressible Euler system coupled to an electromagnetic field. Assuming smallness hypotheses for the…

Analysis of PDEs · Mathematics 2017-05-23 Xavier Blanc , Bernard Ducomet , Sarka Necasova

We study the resolution of discontinuous singularities in gas dynamics via rarefaction waves. The mechanism is well-understood in the one dimensional case. We will prove the non-nonlinear stability of the Riemann problem for…

Analysis of PDEs · Mathematics 2024-09-20 Tian-Wen Luo , Pin Yu

We present a rigorous approach and related techniques to construct global solutions of the 2-D Riemann problem with four-shock interactions for the Euler equations for potential flow. With the introduction of three critical angles: the…

Analysis of PDEs · Mathematics 2023-05-25 Gui-Qiang G. Chen , Alexander Cliffe , Feimin Huang , Song Liu , Qin Wang