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math.AP2024
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…
math.AP2024
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…
math.AP2024
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…