6 papers
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…
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…
Doubly Connected V-States in Geophysical Models: A General Framework
Taoufik Hmidi, Liutang Xue, Zhilong Xue
In this paper, we prove the existence of doubly connected V-states (rotating patches) close to an annulus for active scalar equations with completely monotone kernels. This provide…
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…
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…
Unified theory on V-states structures for active scalar equations
Taoufik Hmidi, Liutang Xue, Zhilong Xue
This paper revolves around the existence of V-states close to Rankine vortices for active scalar equations with completely monotone kernels. This allows to unify various results on…