Exact controllability of the vortex system by means of a single vortex

Justine Dorsz (1, 2) , Olivier Glass (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CIRED - Centre International de Recherche sur l'Environnement et le Développement

In this paper, we investigate the controllability of the point vortex system by means of a single vortex. The point vortex system is a well-known simplied model for the incompressible Euler equation, where the vorticity is concentrated in a nite number of Dirac masses. We use one of the vortices as a control, and prove that by suitably choosing its trajectory, we can drive all other vortices to a given prescribed position in arbitrary time.

Domaines: Optimisation et contrôle [math.OC]

Justine Dorsz, Olivier Glass. Exact controllability of the vortex system by means of a single vortex. 2022. ⟨hal-03775408⟩