Special Session 158: From PDE control to the qualitative study of (random) dynamical systems

On the controllability of the semi-geostrophic equation. Part II
Vincent Laheurte
Universit\`e du Luxembourg
Luxembourg
Co-Author(s):    
Abstract:
Following the first part of this talk by Franck Sueur, I will present some controllability issues for the two-dimensional dual semi-geostrophic equation, a fully nonlinear counterpart of the incompressible Euler equations, where the linear Biot-Savart law is replaced by the nonlinear Monge-Amp\`ere equation. For solutions near the equilibrium state, and through a long-time rescaling, one may establish a connection with the Euler equations. By exploiting this link, I will describe how to recover controllability results (Lagrangian and Eulerian) for the dual semi-geostrophic equation.