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

2021/07/05 by Lucas Ertzbischoff, Ertzbischoff, Lucas
Mathematics · Engineering · #Navier-Stokes equation solutions #Gas Dynamics and Kinetic Theory #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2107.02200

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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