Point vortex for the lake equations
I will start by presenting the lake equations which can be considered as a generalization of the 3D axisymmetric Euler equations without swirl. This 2D model differs from the well-known 2D Euler equations due to an anelastic constraint in the div-curl problem. I will explain how this new constraint implies a very different behavior of concentrated vortices: the point vortex moves under its own influence according to a binormal curvature law. This work is done in collaboration with Lars Eric Hientzsch and Evelyne Miot.
Bio: Christophe Lacave is a French mathematician. He obtained his PhD in 2008 at the University of Lyon 1, under the supervision of Dragos Iftimie. He held a position of maître de conférence (permanent position similar to assistant professor) at the University of Paris Diderot in 2009. Since 2016, he has held a position as a maître de conférence at the University of Grenoble. He is working on the mathematical analysis of partial differential equations, more precisely on the equations of fluid mechanics. To study these equations coming from physics, he use various mathematical theories (on the boundary between complex analysis, elliptic problems, integration theory, compactness
results, numerical analysis).
A first part of his results concerns the convergence of solutions of the 2D Euler equations when the geometry of the domain is perturbed. According to the perturbation, we obtain stability or a limit verifying a modified Euler equation. A second part of his works deals with the question of uniqueness of solutions for these modified limit systems. He has also studied the stability of solutions for the Navier-Stokes equations.
https://www-fourier.univ-grenoble-alpes.fr/~lacavec/index-en.html