Local null-controllability of the 2-D Vlasov-Navier-Stokes system

Iván Moyano (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity field of the fluid from any initial state to the zero steady state, by means of an internal control. Indeed, we can modify the non-linear dynamics of the system in order to absorb the particles and let the fluid at rest. The proof is achieved thanks to the return method and a Leray-Schauder fixed-point argument.

Mots clés: Vlasov-Navier-Stokes system; kinetic theory; kinetic-fluid model; controllability; return method

Domaines: Equations aux dérivées partielles [math.AP]

Iván Moyano. Local null-controllability of the 2-D Vlasov-Navier-Stokes system. 2016. ⟨hal-01346787⟩