3D rotating patches for the 3D quasi-geostrophic model

par Claudia García (Universidad de Granada et IRMAR, Université de Rennes 1)

mardi 2 févr. 2021, 14:00 → 15:00 Europe/Paris

Salle Fokko du Cloux (ICJ)

In this talk, we aim to study time periodic solutions for 3D inviscid quasi-geostrophic model. We show the existence of non trivial rotating patches by suitable perturbation of stationary solutions given by generic revolution shapes around the vertical axis. The construction of those special solutions are done through bifurcation theory. In general, the spectral problem is very delicate and strongly depends on the shape of the initial stationary solutions. Indeed, the spectral study can be related to an eigenvalue problem of a self-adjoint compact operator and we are able to implement the bifurcation only from the largest eigenvalues of such operator which are simple. This is a joint work with T. Hmidi and J. Mateu.