English

Unified theory on V-states structures for active scalar equations

Analysis of PDEs 2023-12-06 v1

Abstract

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 this topic related to geophysical flows. A key ingredient is a new factorization formula for the spectrum using a universal function which is independent of the model. This function admits several interesting properties allowing to track the spectrum distribution.

Keywords

Cite

@article{arxiv.2312.02874,
  title  = {Unified theory on V-states structures for active scalar equations},
  author = {Taoufik Hmidi and Liutang Xue and Zhilong Xue},
  journal= {arXiv preprint arXiv:2312.02874},
  year   = {2023}
}

Comments

48 pages

R2 v1 2026-06-28T13:41:49.981Z