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We investigate the relation between several generalized solution concepts for nonlinear PDE systems from fluid dynamics. More precisely, we study measure-valued solutions, dissipative weak solutions, and energy-variational solutions. For…

Analysis of PDEs · Mathematics 2026-04-02 Thomas Eiter , Robert Lasarzik , Emil Wiedemann

This paper is a follow-up of the work initiated in [3], where it has been investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two…

Probability · Mathematics 2015-06-18 Gioia Carinci , Anna De Masi , Cristian Giardinà , Errico Presutti

The $n$-species particle-exchange process (PEP($n$)) is an exclusion process in which particles of $n$ different species exchange positions on neighbouring sites with rates chosen such that the invariant measure on the discrete torus is a…

Statistical Mechanics · Physics 2026-05-11 Gunter M. Schutz , Ali Zahra

We consider the hydrodynamic modes for dense trapped ultracold gases, where the interparticle distance is comparable to the scattering length. We show that the experimental determination of the hydrodynamic mode frequencies allows to obtain…

Soft Condensed Matter · Physics 2009-11-07 R. Combescot , X. Leyronas

We consider a class of generalized long-range exclusion processes evolving either on $\mathbb Z$ or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and…

Probability · Mathematics 2024-10-24 Patrícia Gonçalves , Julian Kern , Lu Xu

Let $\Lambda$ be a connected closed region with smooth boundary contained in the $d$-dimensional continuous torus $\bb T^d$. In the discrete torus $N^{-1} \bb T^d_N$, we consider a nearest neighbor symmetric exclusion process where…

Probability · Mathematics 2010-05-19 Tertuliano Franco , Adriana Neumann , Glauco Valle

We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The…

Mathematical Physics · Physics 2016-09-29 Stamatis Dostoglou , Jianfei Xue

An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second…

A case can be made that the utility of quasi-linear systems of conservation laws as physical models is largely limited to Euler system models of fluid flow, at least in higher dimensions. Qualified corroboration of this conjecture is…

Analysis of PDEs · Mathematics 2025-09-26 Michael Sever

Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…

Analysis of PDEs · Mathematics 2023-06-02 Renjun Duan , Dongcheng Yang , Hongjun Yu

We consider weak solutions to the incompressible Euler equations. It is shown that energy conservation holds in any Onsager critical class in which smooth functions are dense. The argument is independent of the specific critical regularity…

Analysis of PDEs · Mathematics 2026-01-08 Luigi De Rosa , Marco Inversi , Matteo Nesi

We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar…

Analysis of PDEs · Mathematics 2025-01-06 Mahieddine Adim , Roberta Bianchini , Vincent Duchêne

The hydrodynamic limit and Newtonian limit are important in the relativistic kinetic theory. We justify rigorously the validity of the two independent limits from the special relativistic Boltzmann equation to the classical Euler equations…

Analysis of PDEs · Mathematics 2023-09-01 Yong Wang , Changguo Xiao

Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then, by considering the same class of infinite interacting…

Probability · Mathematics 2021-06-08 Joe P. Chen , Federico Sau

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

We study the hydrodynamic limit for the isothermal dynamics of an anharmonic chain under hyperbolic space-time scaling under varying tension. The temperature is kept constant by a contact with a heat bath, realised via a stochastic…

Probability · Mathematics 2019-05-28 Stefano Marchesani , Stefano Olla

The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk. More…

Probability · Mathematics 2020-10-23 Clément Erignoux , Patricia Gonçalves , Gabriel Nahum

We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler…

Probability · Mathematics 2019-01-08 Cédric Bernardin , François Huveneers , Stefano Olla

We obtain the hydrodynamic limit of symmetric long-jumps exclusion in $\mathbb{Z}^d$ (for $d \geq 1$), where the jump rate is inversely proportional to a power of the jump's length with exponent $\gamma+1$, where $\gamma \geq 2$. Moreover,…

Probability · Mathematics 2024-06-11 Pedro Cardoso , Patrícia Gonçalves , Byron Jiménez-Oviedo

We rigorously show a large friction limit of hydrodynamic models with alignment, attractive, and repulsive effects. More precisely, we consider pressureless Euler equations with nonlocal forces and provide a quantitative estimate of large…

Analysis of PDEs · Mathematics 2020-09-29 Young-Pil Choi