报告地点：行健楼学术活动室526
Abstract:
We investigate the long-time dynamics of finite-energy weak solutions to the Vlasov–Navier–Stokes system on a two-dimensional torus. We first analyze the homogeneous setting—an incompressible viscous fluid of constant density coupled to dispersed particles—and then treat variable-density flows. In both regimes, we show that the particle distribution converges to a monokinetic equilibrium. More precisely, for incompressible Vlasov–Navier–Stokes with finite-energy initial data, we establish explicit algebraic decay of global weak solutions; when the initial particle distribution is sufficiently small, the decay becomes exponential. This refines the result of Han–Kwan, Mossa and Moyano (2020) by removing the smallness assumption on the fluid velocity. In the non-homogeneous case, we obtain analogous stability and convergence for flows allowing piecewise constant fluid densities with jumps. This work is in collaboration with Prof. Raphaël Danchin.
