Prescribing the motion of a set of particles in a 3D perfect fluid

Olivier Glass (1) , Thierry Horsin (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LMV - Laboratoire de Mathématiques de Versailles
3 M2N - Modélisation mathématique et numérique

We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R^3 and two smooth contractible sets of fluid particles, surrounding the same volume. We prove that given any initial velocity field, one can find a boundary control and a time interval such that the corresponding solution of the Euler equation makes the first of the two sets approximately reach the second one.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Olivier Glass, Thierry Horsin. Prescribing the motion of a set of particles in a 3D perfect fluid. SIAM Journal on Control and Optimization, 2012, 50 (5), pp.2726-2742. ⟨10.1137/110845744⟩. ⟨hal-00616872⟩