8 papers
Isothermal hydrodynamic limit for kinetic flocking models with nonlinear velocity alignment
Roman Shvydkoy, Changhui Tan
We study the hydrodynamic limit of kinetic flocking models with nonlinear velocity alignment and strong local Fokker--Planck forcing. In the limit of small Knudsen number the kinet…
Mean-Field Limits of Deterministic and Stochastic Flocking Models with Nonlinear Velocity Alignment
Vinh Nguyen, Roman Shvydkoy, Changhui Tan
We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol and…
Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force
Roman Shvydkoy, Trevor Teolis
We study a coupled Fokker-Planck--Navier-Stokes (FPNS) system modeling the dynamics of interacting particles suspended in a viscous incompressible fluid, where the coupling occurs…
Modulation of the Monokinetic Limit for Models of Collective Dynamics
Alina Chertock, Roman Shvydkoy, Trevor Teolis
In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a…
Global well-posedness and relaxation for solutions of the Fokker-Planck-Alignment equations
R. Shvydkoy
In this paper we prove global existence of weak solutions, their regularization, and relaxation for large data for a broad class of Fokker-Planck-Alignment models which appear in c…
Microscopic, mesoscopic, and macroscopic descriptions of the Euler alignment system with adaptive communication strength
Roman Shvydkoy, Trevor Teolis
This is a continuation of our previous joint work on the $\st$-model in[\textit{Well-posedness and long time behavior of the Euler Alignment System with adaptive communication stre…
Well-posedness and Long Time Behavior of the Euler Alignment System with Adaptive Communication Strength
Roman Shvydkoy, Trevor Teolis
We study a new flocking model which has the versatility to capture the physically realistic qualitative behavior of the Motsch-Tadmor model, while also retaining the entropy law, w…
Generic alignment conjecture for systems of Cucker-Smale type
Roman Shvydkoy
The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker-Smale system with a strictly local communication align to the common…