Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

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

Résumé

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.
Fichier principal
Vignette du fichier
main.pdf (675.25 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04370483 , version 1 (04-01-2024)

Identifiants

Citer

Dimitri Cobb, Martin Donati, Ludovic Godard-Cadillac. Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex. 2024. ⟨hal-04370483⟩
26 Consultations
36 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More