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. C…
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.AP2022
Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc
Taoufik Hmidi, Liutang Xue, Zhilong Xue
In this paper we address the existence of time periodic solutions for the generalized inviscid SQG equation in the unit disc with homogeneous Dirichlet boundary condition when $α\i…