English
Related papers

Related papers: Hydrodynamic Cucker-Smale model with normalized co…

200 papers

We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The…

Analysis of PDEs · Mathematics 2019-02-01 P. Aceves-Sánchez , M. Bostan , J. A. Carrillo , P. Degond

We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the…

Analysis of PDEs · Mathematics 2015-05-27 Sebastien Motsch , Eitan Tadmor

We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…

Analysis of PDEs · Mathematics 2016-04-19 Young-Pil Choi , Bongsuk Kwon

We study a pressureless Euler system with a nonlinear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density…

Analysis of PDEs · Mathematics 2017-11-22 Tam Do , Alexander Kiselev , Lenya Ryzhik , Changhui Tan

We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker-Smale model with a confining potential in a…

Analysis of PDEs · Mathematics 2025-08-26 Ning Jiang , Yi-Long Luo , Teng-Fei Zhang

We study the emergent behaviors of the weak solutions to the kinetic Cucker-Smale (in short, KCS) model in a non-compact spatial-velocity support setting. Unlike the compact support situation, non-compact support of a weak solution can…

Analysis of PDEs · Mathematics 2026-04-21 Seung-Yeal Ha , Xinyu Wang

In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…

Analysis of PDEs · Mathematics 2021-02-10 Roberto Natalini , Thierry Paul

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights $\phi_\alpha(x) = |x|^{-\alpha}$ for some $\alpha > 0$. We consider a kinetic BGK-alignment model consisting of a…

Analysis of PDEs · Mathematics 2023-03-22 Young-Pil Choi , Byung-Hoon Hwang

We present a Cucker-Smale (C-S) type flocking model on a sphere. We study velocity alignment on a sphere and prove the emergence of flocking for the proposed model. Our model includes three new terms: a centripetal force, multi-agent…

Dynamical Systems · Mathematics 2020-10-22 Sun-Ho Choi , Dohyun Kwon , Hyowon Seo

This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…

Analysis of PDEs · Mathematics 2018-01-16 Young-Pil Choi

We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension $N=2,3$. These models arise in the…

Analysis of PDEs · Mathematics 2015-12-11 José A. Carrillo , Eduard Feireisl , Piotr Gwiazda , Agnieszka Świerczewska-Gwiazda

In this paper, we discuss the flocking phenomenon for the Cucker-Smale and Motsch-Tadmor models in continuous time on a general oriented and weighted graph with a general communication function. We present a new approach for studying this…

Probability · Mathematics 2022-08-05 Adrien Jean Cotil

In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. The solutions describe unidirectional…

Analysis of PDEs · Mathematics 2020-02-17 Daniel Lear , Roman Shvydkoy

We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…

Analysis of PDEs · Mathematics 2019-05-22 Javier Morales , Jan Peszek , Eitan Tadmor

We study the large-time behavior of hydrodynamic model which describes the collective behavior of continuum of agents, driven by pairwise alignment interactions with additional external potential forcing. The external force tends to compete…

Analysis of PDEs · Mathematics 2020-07-15 Ruiwen Shu , Eitan Tadmor

We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…

Analysis of PDEs · Mathematics 2007-12-27 Jerry L. Bona , David Lannes , Jean-Claude Saut

Consider a system of autonomous interacting agents moving in space, adjusting each own velocity as a weighted mean of the relative velocities of the other agents. In order to test the robustness of the model, we assume that each pair of…

Probability · Mathematics 2014-05-05 Eduardo Canale , Federico Dalmao , Ernesto Mordecki , Max Souza

In particle systems, flocking refers to the phenomenon where particles' individual velocities eventually align. The Cucker-Smale model is a well-known mathematical framework that describes this behavior. Many continuous descriptions of the…

Analysis of PDEs · Mathematics 2024-07-29 Sebastian Zimper , Federico Cornalba , Nataša Djurdjevac Conrad , Ana Djurdjevac

Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical…

Numerical Analysis · Mathematics 2007-05-23 Colin Cotter

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for…

Analysis of PDEs · Mathematics 2024-10-29 D. Amadori , F. A. Chiarello , C. Christoforou