4 papers
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…
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.…
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…
Local regularity and finite-time singularity for a class of generalized SQG patches on the half-plane
Qianyun Miao, Changhui Tan, Liutang Xue +1
In this paper, we investigate a class of inviscid generalized surface quasi-geostrophic (SQG) equations on the half-plane with a rigid boundary. Compared to the Biot-Savart law in…