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arXiv · 2107.02200

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

Lucas Ertzbischoff
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Abstract

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.

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Lucas Ertzbischoff. 2021-07-05. Decay and absorption for the Vlasov-Navier-Stokes system with gravity in a half-space. https://arxiv.org/abs/2107.02200

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