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math.AP2026
Local well-posedness for a moving rigid region in Surface Quasi-Geostrophic equations
Ludovic Godard-Cadillac, Arnab Roy
We introduce and analyze a class of Surface Quasi-Geostrophic (SQG) equations in the presence of moving rigid obstacles. The model is motivated both by vortex-wave type asymptotics…
math.AP2024
On the Dynamics of Point Vortices with Positive Intensities collapsing with the boundary
Martin Donati, Ludovic Godard-Cadillac, Dragos Iftimie
In this paper, we study the point-vortex dynamics with positive intensities. We show that in the half-plane and in a disk, collapses of point vortices with the boundary in finite t…
math.AP2024
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
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…