[PDF][PDF] Unified theory on v-states structures for active scalar equations
T Hmidi, L Xue, Z Xue - arXiv preprint arXiv:2312.02874, 2023 - researchgate.net
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 …
scalar equations with completely monotone kernels. This allows to unify various results on …
Local regularity and finite-time singularity for a class of generalized SQG patches on the half-plane
Q Miao, C Tan, L Xue, Z Xue - arXiv preprint arXiv:2410.19273, 2024 - arxiv.org
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 the …
equations on the half-plane with a rigid boundary. Compared to the Biot-Savart law in the …
Eulerian uniqueness of the -SQG patch problem
X Luo - arXiv preprint arXiv:2403.04219, 2024 - arxiv.org
We consider the patch problem of the $\alpha $-SQG equation with $\alpha= 0$ being the
2D Euler and $\alpha=\frac {1}{2} $ the SQG equations respectively. In the Eulerian setting …
2D Euler and $\alpha=\frac {1}{2} $ the SQG equations respectively. In the Eulerian setting …