Controls insensitizing the observation of a quasi-geostrophic ocean model

Abstract

We consider a linear quasi-geostrophic ocean model with partially known initial conditions. We search for controls that make the observation locally insensitive to the perturbations of the initial data. Their existence is equivalent to the null controllability property for an associated cascade Stokes-like system. Thanks to the presence of the Coriolis term, we are able to prove the existence of such controls. Our strategy is the following. First, we prove a unique continuation property for the adjoint of the state system that leads to approximate controllability; then, under certain assumptions, an observability inequality is established for the adjoint. The proof is inspired by the arguments leading to the unique continuation property. This inequality leads to the desired null controllability result.