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arXiv · 2401.02728

Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex

Dimitri Cobb·Martin Donati·Ludovic Godard-Cadillac
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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.

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Dimitri Cobb, Martin Donati, Ludovic Godard-Cadillac. 2024-01-05. Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex. https://arxiv.org/abs/2401.02728

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