Local null controllability of a rigid body moving into a Boussinesq flow

Arnab Roy (1) , Takéo Takahashi (2, 3)

1 TIFR-CAM - Center for Applicable Mathematics [Bangalore]
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 IECL - Institut Élie Cartan de Lorraine

In this paper, we study the controllability of a fluid-structure interaction system. We consider a viscous and incompressible fluid modeled by the Boussinesq system and the structure is a rigid body with arbitrary shape which satisfies Newton's laws of motion. We assume that the motion of this system is bidimensional in space. We prove the local null controllability for the velocity and temperature of the fluid and for the position and velocity of rigid body for a control acting only on the temperature equation on a fixed subset of the fluid domain.

Mots clés: Navier-Stokes equations; Fluid-structure interaction; Boussinesq; Carleman inequality; Rigid body; Controllability; system

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

Arnab Roy, Takéo Takahashi. Local null controllability of a rigid body moving into a Boussinesq flow. Mathematical Control and Related Fields, 2019, 9 (4), pp.793-836. ⟨10.3934/mcrf.2019050⟩. ⟨hal-01572508⟩