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We propose and study a nonlocal Euler system with relaxation, which tends to a strictly hyperbolic system under the hyperbolic scaling limit. An independent proof of the local existence and uniqueness of this system is presented in any…

Analysis of PDEs · Mathematics 2020-10-07 Manas Bhatnagar , Hailiang Liu

Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale…

Analysis of PDEs · Mathematics 2025-11-25 Ziming Bian , Seung-Yeal Ha , Tommaso Ruggeri , Qinghua Xiao

We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment…

Analysis of PDEs · Mathematics 2020-04-09 Qianyun Miao , Changhui Tan , Liutang Xue

We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle…

Analysis of PDEs · Mathematics 2021-03-17 Razvan C. Fetecau , Hansol Park , Francesco S. Patacchini

In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…

Optimization and Control · Mathematics 2020-11-18 Wouter Baar , Dario Bauso

We consider the Cucker-Smale system with multiplicative noise in a harmonic potential field and investigate the effect of harmonic potential field. In the presence of external potential force, the system is expected to emerge into almost…

Dynamical Systems · Mathematics 2022-05-27 Du Linglong , Zhou Xinyun

We study the Euler Alignment system of collective behavior, equipped with `topological' interaction protocols, which were introduced to the mathematical literature by Shvydkoy and Tadmor. Interactions subject to these protocols may depend…

Analysis of PDEs · Mathematics 2026-05-29 Trevor M. Leslie , Jan Peszek

Flocking behavior has attracted considerable attention in multi-agent systems. The structure of flocking has been predominantly studied through the application of artificial potential fields coupled with velocity consensus. These…

Optimization and Control · Mathematics 2020-08-21 Logan E. Beaver , Chris Kroninger , Andreas A. Malikopoulos

We investigate the large-time behavior of the pressureless Euler system with nonlocal velocity alignment and interaction forces, with the aim of characterizing the asymptotic convergence of classical solutions under general interaction…

Analysis of PDEs · Mathematics 2025-10-29 José A. Carrillo , Young-Pil Choi , Dowan Koo , Oliver Tse

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…

Probability · Mathematics 2024-06-13 Jacob Calvert , Dana Randall

Using a minimal aggregation-based model, we address the efficient information transfer observed in natural flocks during collective turns. Specifically, we demonstrate that this feature can arise solely from the non-reciprocal nature of…

Adaptation and Self-Organizing Systems · Physics 2025-11-25 Joao Lizárraga , Marcus de Aguiar

This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…

Analysis of PDEs · Mathematics 2023-05-10 Marc Briant , Nicolas Meunier

Crowd dynamics and many large biological systems can be described as populations of agents or particles, which can only be observed on aggregate population level. Identifying the dynamics of agents is crucial for understanding these large…

Optimization and Control · Mathematics 2025-03-18 Filip Elvander , Isabel Haasler

We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities together with a continuity argument, we…

Dynamical Systems · Mathematics 2017-12-05 Young-Pil Choi , Zhuchun Li

Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where…

Adaptation and Self-Organizing Systems · Physics 2012-01-16 Nicholas A. Mecholsky , Edward Ott , Thomas M. Antonsen , Parvez Guzdar

We establish the large-time behavior for the coupled kinetic-fluid equations. More precisely, we consider the Vlasov equation coupled to the compressible isentropic Navier-Stokes equations through a drag forcing term. For this system, the…

Analysis of PDEs · Mathematics 2016-08-03 Young-Pil Choi

We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of…

Analysis of PDEs · Mathematics 2020-01-08 Daniel Ginsberg , Hans Lindblad , Chenyun Luo

In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles increases beyond a certain threshold. In this paper, we argue that such a threshold…

Soft Condensed Matter · Physics 2010-03-29 Chiu Fan Lee

We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large…

Analysis of PDEs · Mathematics 2018-03-06 Manas Ranjan Sahoo , Abhrojyoti Sen

This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…

Analysis of PDEs · Mathematics 2007-05-23 G. Loeper
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