Decay and absorption for the Vlasov-Navier-Stokes system with gravity in a half-space

Lucas Ertzbischoff (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

This paper is devoted to the large time behavior of weak solutions to the three-dimensional Vlasov-Navier-Stokes system set on the half-space, with an external gravity force. This fluid-kinetic coupling arises in the modeling of sedimentation phenomena. We prove that the local density of the particles and the fluid velocity enjoy a convergence to 0 in large time and at a polynomial rate. In order to overcome the effect of the gravity, we rely on a fine analysis of the absorption phenomenon at the boundary. We obtain a family of decay estimates for the moments of the kinetic distribution, provided that the initial distribution function has a sufficient decay in the phase space.

Domaines: Mathématiques [math]

Lucas Ertzbischoff. Decay and absorption for the Vlasov-Navier-Stokes system with gravity in a half-space. 2021. ⟨hal-03281075⟩