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We consider a compressible Euler system with singular velocity alignment, known as the Euler-alignment system, describing the flocking behaviors of large animal groups. We establish a local well-posedness theory for the system, as well as a…

Analysis of PDEs · Mathematics 2020-07-17 Li Chen , Changhui Tan , Lining Tong

We study the emergent dynamics of the relativistic kinetic Cucker-Smale (RKCS) model without assuming compactness in spatial and velocity support. In this setting, the lower bound of the kernel function in the nonlocal velocity alignment…

Analysis of PDEs · Mathematics 2025-07-11 Seung-Yeal Ha , Xinyu Wang

We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale equation in the one-dimensional case. We propose an…

Analysis of PDEs · Mathematics 2022-08-01 Jan Peszek , David Poyato

We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the…

Analysis of PDEs · Mathematics 2020-07-14 Young-Pil Choi , Kyungkeun Kang , Hwa Kil Kim , Jae-Myoung Kim

Classical swarm models, exemplified by the Cucker--Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems.…

Adaptation and Self-Organizing Systems · Physics 2025-09-08 Rene Fabregas , Jie Liao , Nisrine Outada

In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not…

Optimization and Control · Mathematics 2025-08-26 Chiara Cicolani , Elisa Continelli , Cristina Pignotti

We consider the kinetic Cucker-Smale model with local alignment as a mesoscopic description for the flocking dynamics. The local alignment was first proposed by Karper, Mellet and Trivisa \cite{K-M-T-3}, as a singular limit of a normalized…

Analysis of PDEs · Mathematics 2018-09-13 Alessio Figalli , Moon-Jin Kang

We prove the existence of weak solutions to kinetic flocking model with cut-off interaction function by using Schauder fixed pointed theorem and velocity averaging lemma. Under the natural assumption that the velocity support of the initial…

Analysis of PDEs · Mathematics 2015-10-07 Chunyin Jin

We present some recent development in modeling concurrent emergence of collective behaviors, namely, the emergence of clustering, flocking and synchronization at the same time. We derive two new models, namely Swarmalator-Vicsek and…

Dynamical Systems · Mathematics 2023-02-15 Trenton Gerew , Ming Zhong

We present collective dynamics of the Cucker-Smale (C-S) ensemble under random communications. As an effective modeling of the C-S ensemble, we introduce a stochastic kinetic C-S equation with a multiplicative white noise. For the proposed…

Analysis of PDEs · Mathematics 2019-09-04 Seung-Yeal Ha , Jinwook Jung , Michael Röckner

A Collision-Avoiding flocking particle system proposed in [8] is studied in this paper. The global wellposedness of its corresponding Vlasov-type kinetic equation is proved. As a corollary of the global stability result, the mean field…

Mathematical Physics · Physics 2013-11-15 Rong Yang , Li Chen

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 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 study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale and Motsch-Tadmor models. We prove flocking behavior for the kinetic descriptions of flocking systems,…

Numerical Analysis · Mathematics 2020-07-20 Changhui Tan

In this paper, a delay Vlasov-Fokker-Planck equation associated to a stochastic interacting particle system with delay is investigated analytically. Under certain restrictions on the parameters well-posedness and ergodicity of the…

Analysis of PDEs · Mathematics 2017-10-06 Axel Klar , Lisa Kreusser , Oliver Tse

We study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a Cucker-Smale type alignment dynamics with compactly supported communication kernels and to…

Mathematical Physics · Physics 2022-12-22 Paolo Buttà , Carlo Marchioro

We investigate consensus formation and flocking behavior in multi-agent systems subject to two distinct types of delays: a transmission delay accounting for information exchange between agents, and a reaction delay representing the…

Dynamical Systems · Mathematics 2026-04-22 Elisa Continelli , Jan Haskovec , Cristina Pignotti

The hydrodynamic limit of a kinetic Cucker-Smale model is investigated. In addition to the free-transport of individuals and the Cucker-Smale alignment operator, the model under consideration includes a strong local alignment term. This…

Analysis of PDEs · Mathematics 2012-06-01 Trygve Karper , Antoine Mellet , Konstantina Trivisa

In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the…

Analysis of PDEs · Mathematics 2020-07-10 José A. Carrillo , Young-Pil Choi , Jinwook Jung

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Qian Feng , Sing Kiong Nguang , Wilfrid Perruquetti