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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 and…
math.AP2025
A revisit of patch solutions for the 2D Loglog-Euler type equation
Changhui Tan, Liutang Xue, Zhilong Xue
In this paper, we revisit the patch solutions for a class of inviscid whole-space active scalar equations that interpolate between the 2D Euler equation and the -SQG equation. C…
math.AP2025
On the Euler-Poisson equations with variable background states and nonlocal velocity alignment
Kunhui Luan, Changhui Tan, Qiyu Wu
We study the 1D pressureless Euler-Poisson equations with variable background states and nonlocal velocity alignment. Our main focus is the phenomenon of critical thresholds, where…