Lucas Ertzbischoff
Published 2021-07-05Version 1
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.
Classification of solutions to $Δu = u^{-γ}$ in the half-space
Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data
The balance between diffusion and absorption in semilinear parabolic equations
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