7 papers · 1 filter
Global regularity for the unidirectional Euler-alignment system with supercritical dissipation
Changhui Tan, Liutang Xue
We prove global well-posedness of the periodic unidirectional Euler-alignment system in every dimension for supercritical dissipation of order and arbitrary non-vacuum init…
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…
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…
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…
On the Aw-Rascle-Zhang traffic models with nonlocal look-ahead interactions
Thomas Hamori, Changhui Tan
We present a new family of second-order traffic flow models, extending the Aw-Rascle-Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal…
Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure
Xiang Bai, Changhui Tan, Liutang Xue
We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth…