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Related papers: Existence of Weak Solutions to Kinetic Flocking Mo…

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We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under consideration include the kinetic Cucker-Smale equation with possibly non-symmetric flocking potential, the Cucker-Smale equation…

Analysis of PDEs · Mathematics 2012-02-21 Trygve Karper , Antoine Mellet , Konstantina Trivisa

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 two recent papers the authors study the existence of weak solutions and the hydrodynamic limit of kinetic flocking equations with strong local alignment. The introduction of a strong local alignment term to model flocking behavior was…

Analysis of PDEs · Mathematics 2012-02-21 Trygve Karper , Antoine Mellet , Konstantina Trivisa

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in [2] to the Cauchy problem for any $BV$ initial data that has…

Analysis of PDEs · Mathematics 2023-09-06 Debora Amadori , Cleopatra Christoforou

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 $\alpha\in(0,2)$. Here, we consider the critical case…

Analysis of PDEs · Mathematics 2021-05-26 Daniel Lear

We study the Cucker-Smale model with a velocity control function. The Cucker-Smale model design the emergence of consensus in terms of flocking. A proposed model encompasses several Cucker-Smale models, such as a speed limit model, a…

Classical Analysis and ODEs · Mathematics 2023-02-08 Junhyeok Byeon

We study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive sufficient conditions for asymptotic flocking of the solutions.…

Dynamical Systems · Mathematics 2020-05-12 Jan Haskovec , Ioannis Markou

We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…

Analysis of PDEs · Mathematics 2025-10-09 Young-Pil Choi , Sihyun Song

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

Analysis of PDEs · Mathematics 2013-11-25 J. A. Carrillo , Y. -P. Choi , T. K. Karper

We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of multiple sclerosis. The model is derived from a general chemotaxis-type framework and describes…

Analysis of PDEs · Mathematics 2026-01-28 S. Fagioli , M. Kamath Katapady

We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…

Probability · Mathematics 2022-03-17 Martin Friesen , Oleksandr Kutoviy

We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…

Analysis of PDEs · Mathematics 2021-12-28 Jan Haskovec

We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the…

Analysis of PDEs · Mathematics 2019-07-16 Young-Pil Choi , Cristina Pignotti

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

The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to aggregate, flock or disperse. The paper examines the kinetic…

Analysis of PDEs · Mathematics 2017-07-19 Piotr B. Mucha , Jan Peszek

We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…

Analysis of PDEs · Mathematics 2026-02-17 Ruicheng Cheng , Seung-Yeal Ha , Jaemoon Lee , Zhenfu Wang

A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…

Analysis of PDEs · Mathematics 2015-12-04 Ansgar Jüngel , Nicola Zamponi

We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the…

Analysis of PDEs · Mathematics 2013-02-19 Jan Peszek

A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic…

Analysis of PDEs · Mathematics 2022-12-06 Li Chen , Yue Li , Nicola Zamponi

We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D.…

Dynamical Systems · Mathematics 2021-01-05 Sun-Ho Choi , Dohyun Kwon , Hyowon Seo
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