Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex
Analysis of PDEs
2025-01-16 v2
Abstract
This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with parameter 0 < s < 1. We obtained local existence of classical solutions in H^4 under the standard ''plateau hypothesis'', H^2-stability of the solutions, and a blow-up criterion. In the sub-critical case s > 1/2 we established global existence of weak solutions. For the critical case s = 1/2, we introduced a weaker notion of solution (V-weak solutions) to give a meaning to the equation and prove global existence.
Keywords
Cite
@article{arxiv.2401.02728,
title = {Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex},
author = {Dimitri Cobb and Martin Donati and Ludovic Godard-Cadillac},
journal= {arXiv preprint arXiv:2401.02728},
year = {2025}
}