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This paper is devoted to the large time behavior of weak solutions to thethree-dimensional Vlasov-Navier-Stokes system set on the half-space, with anexternal gravity force. This fluid-kinetic coupling arises in the modeling ofsedimentation phenomena. We prove that the local density of the particles andthe fluid velocity enjoy a convergence to $0$ in large time and at a polynomialrate. In order to overcome the effect of the gravity, we rely on a fineanalysis of the absorption phenomenon at the boundary. We obtain a family ofdecay estimates for the moments of the kinetic distribution, provided that theinitial distribution function has a sufficient decay in the phase space.

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