相关论文: Singular Cucker-Smale Dynamics
We study the Cucker--Smale (C-S) flocking systems involving both singularity and noise. We first show the local strong well-posedness for the stochastic singular C-S systems before the first collision time, which is a well defined stopping…
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…
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…
We prove that certain types of measure-valued mappings are monokinetic i.e. the distribution of velocity is concentrated in a Dirac mass. These include weak measure-valued solutions to the strongly singular Cucker-Smale model with…
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…
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…
We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler…
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…
Collision avoidance is an interesting feature of the Cucker-Smale (CS) model of flocking that has been studied in many works, e.g. [1, 2, 4, 6, 7, 20, 21, 22]. In particular, in the case of singular interactions between agents, as is the…
We consider the Cucker-Smale flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$ with $\alpha > 0$. We provide a critical value of the exponent $\alpha$ in the communication weight leading to global regularity of…
We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate…
We present the relativistic analogue of the Cucker-Smale model with a bonding force on Riemannian manifold, and study its emergent dynamics. The Cucker-Smale model serves a prototype example of mechanical flocking models, and it has been…
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…
We prove the lack of asymptotic collisions between particles following the Cucker-Smale flocking model with a bonding force and its simplification. Moreover, we prove that in the case of the CSB model with a singular communication weight,…
We analyze the one dimensional Cucker-Smale (in short CS) model with a weak singular communication weight $\psi(x) = |x|^{-\beta}$ with $\beta \in (0,1)$. We first establish a global-in-time existence of measure-valued solutions to the…
We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid $\mathbb{H}^d$ in any dimensions. In a recent work \cite{H-H-K-K-M}, a first-order aggregation model on the hyperboloid was proposed and its emergent dynamics was…
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…
In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the…
We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic…
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…