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In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…

Analysis of PDEs · Mathematics 2015-03-03 Liutang Xue

We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a…

Probability · Mathematics 2012-01-12 François Bolley , José Alfredo Cañizo , José Antonio Carrillo

We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. Under minimal structural assumptions on the graph, we…

Analysis of PDEs · Mathematics 2026-05-15 Elvise Berchio , Davide Bianchi , Alberto G. Setti , Maria Vallarino

We here investigate a modification of the compressible barotropic Euler system with friction, involving a fuzzy nonlocal pressure term in place of the conventional one. This nonlocal term is parameterized by $\epsilon$ > 0 and formally…

Analysis of PDEs · Mathematics 2023-12-13 Raphael Danchin , Piotr Boguslaw Mucha

We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…

Analysis of PDEs · Mathematics 2025-03-18 Jesus Correa , Christian Olivera

We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…

High Energy Physics - Theory · Physics 2007-05-23 Z. Haba

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…

Soft Condensed Matter · Physics 2009-11-11 Thomas Ihle , Erkan Tuzel , Daniel M. Kroll

Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…

Analysis of PDEs · Mathematics 2018-03-12 José A. Carrillo , Aneta Wróblewska-Kamińska , Ewelina Zatorska

We introduce a variational time discretization for the multi-dimensional gas dynamics equations, in the spirit of minimizing movements for curves of maximal slope. Each timestep requires the minimization of a functional measuring the…

Analysis of PDEs · Mathematics 2018-10-01 Fabio Cavalletti , Marc Sedjro , Michael Westdickenberg

We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces…

Analysis of PDEs · Mathematics 2022-03-31 José A. Carrillo , Young-Pil Choi , Oliver Tse

We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices.…

Mathematical Physics · Physics 2020-10-21 Matthew Rosenzweig

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force. When the magnetic field is large, the so-called drift-fluid approximation is obtained. In this…

Mathematical Physics · Physics 2014-04-08 Pierre Degond , Fabrice Deluzet , Afeintou Sangam , Marie-Hélène Vignal

We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…

Analysis of PDEs · Mathematics 2015-12-17 Fatiha Alabau-Boussouira , Yannick Privat , Emmanuel Trélat

We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…

Analysis of PDEs · Mathematics 2026-05-08 Chenyun Luo , Junyan Zhang

The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and…

Optics · Physics 2015-05-19 T. G. Philbin

We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…

Analysis of PDEs · Mathematics 2025-02-12 Didier Bresch , Mitia Duerinckx , Pierre-Emmanuel Jabin

We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with H\"older noise and potential whose range is large in comparison with the typical distance between…

Analysis of PDEs · Mathematics 2025-02-25 Jesus Correa , Juan Londoño , Christian Olivera

We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of the continuum model are a nonlocal term and Q-Wiener process…

Numerical Analysis · Mathematics 2022-04-05 Georgi Medvedev , Gideon Simpson

We consider a microscopic model of spherical particles with inertia in a Stokes flow. As the particle number grows to infinity and their size goes to zero we derive the monokinetic Vlasov-Stokes equations as mean-field limit. We do this…

Analysis of PDEs · Mathematics 2025-11-19 Richard M. Höfer , A. Mecherbet , R. Schubert

We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…

Analysis of PDEs · Mathematics 2020-02-17 Ryan Hynd