3 papers
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.…
math.AP2025
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…
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…