6 papers · 1 filter
Uniformly Rotating Vortex Patches with Arbitrarily Many Genuine Holes
Zhilong Xue, Weicheng Zhan
For every prescribed integer , we construct uniformly rotating unit-vorticity vortex patches for the planar Euler equation such that is connected 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…
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…
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…
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…