Existence and Uniqueness for the SQG Vortex-Wave System when the Vorticity is Constant near the Point-Vortex
DONATI, Martin
École normale supérieure de Lyon [ENS de Lyon]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
École normale supérieure de Lyon [ENS de Lyon]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
GODARD-CADILLAC, Ludovic
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
DONATI, Martin
École normale supérieure de Lyon [ENS de Lyon]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
École normale supérieure de Lyon [ENS de Lyon]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
GODARD-CADILLAC, Ludovic
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Institut Polytechnique de Bordeaux [Bordeaux INP]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Document de travail - Pré-publication
This item was published in
2024-01-03
English 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 ...Read more >
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.Read less <
English Keywords
Vortex Interaction
Quasi-geostrophic dynamics
Evolution equation nonlinear
PDE Modeling
Origin
Hal imported