activity
20242026
collaborators

7 papers

math.AP2026

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…

math.AP2025

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 an…

math.AP2025

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…

math.DS2025

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…

math.AP2025

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…

math.AP2025

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…