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Related papers: High-friction limit for bipolar Euler-Riesz system…

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Several recent papers considered the high-friction limit for systems arising in fluid mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard equation as a limit of the nonlocal Euler-Korteweg equation using the…

Analysis of PDEs · Mathematics 2023-08-24 Charles Elbar , Piotr Gwiazda , Jakub Skrzeczkowski , Agnieszka Świerczewska-Gwiazda

The derivation of an approximate Class-I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class-II model is justified, by validating the Chapman-Enskog expansion performed from the Class-II model…

Analysis of PDEs · Mathematics 2024-05-24 Stefanos Georgiadis , Athanasios E. Tzavaras

The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of…

Dynamical Systems · Mathematics 2016-11-24 Jan Březina , Václav Mácha

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 investigate the large-friction and incompressible limits for a two-phase flow (Euler-NS) system which couples the pressureless Euler equations and the isentropic compressible Navier-Stokes equations through a drag force term with the…

Analysis of PDEs · Mathematics 2025-08-29 Hai-Liang Li , Ling-Yun Shou , Yue Zhang

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

We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use…

Analysis of PDEs · Mathematics 2017-09-08 Jan Giesselmann , Athanasios E. Tzavaras

In this paper we study weak-strong uniqueness and singular relaxation limits for the Euler--Korteweg and Navier--Stokes--Korteweg systems with non monotone pressure. Both weak-strong uniqueness and the relaxation limit are investigated…

Analysis of PDEs · Mathematics 2025-09-10 Giada Cianfarani Carnevale , Jan Giesselmann

We are concerned with a system governing the evolution of the pressureless compressible Euler equations with Riesz interaction and damping in $\mathbb{R}^{d}$ ($d\geq1$), where the interaction force is given by…

Analysis of PDEs · Mathematics 2024-07-01 Meiling Chi , Ling-Yun Shou , Jiang Xu

Euler alignment systems appear as hydrodynamic limits of interacting self-propelled particle systems such as the (generalized) Cucker-Smale model. In this work, we study weak solutions to an Euler alignment system on smooth, bounded,…

Analysis of PDEs · Mathematics 2023-05-24 Amoolya Tirumalai , Christos Mavridis , John S. Baras

In this paper, we consider the dispersive limit of the Euler-Poisson system for ion-acoustic waves. We establish that under the Gardner-Morikawa type transformations, the solutions of the Euler-Poisson system converge globally to the…

Mathematical Physics · Physics 2013-04-30 Xueke Pu

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…

Analysis of PDEs · Mathematics 2020-01-03 Eduard Feireisl , Martina Hofmanová

We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…

Analysis of PDEs · Mathematics 2015-06-04 Tianwen Luo , Chunjing Xie , Zhouping Xin

In this article, the weak-strong uniqueness principle is proved for an Euler-Poisson system in the whole space, with initial data so that the strong solution exists. Some results on Riesz potentials are used to justify the considered weak…

Analysis of PDEs · Mathematics 2024-04-16 Nuno J. Alves

We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…

Statistical Mechanics · Physics 2021-01-01 Frederik S. Møller , Gabriele Perfetto , Benjamin Doyon , Jörg Schmiedmayer

We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…

Probability · Mathematics 2024-11-13 Patrick van Meurs , Kenkichi Tsunoda , Lu Xu

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional…

Analysis of PDEs · Mathematics 2021-03-22 Corrado Lattanzio , Athanasios E. Tzavaras

We investigate the dynamics of short-range interacting Bose gases with varying degrees of diluteness and interaction strength. By applying a combined mean-field and semiclassical space-time rescaling to the dynamics in both the…

Analysis of PDEs · Mathematics 2025-03-07 Jacky Chong , Shunlin Shen , Zhifei Zhang

A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The…

Analysis of PDEs · Mathematics 2023-02-23 Tomáš Roubíček

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow…

Analysis of PDEs · Mathematics 2021-03-22 Corrado Lattanzio , Athanasios E. Tzavaras