题目：Convergence to equilibrium states in two-dimensional Vlasov-Navier-Stokes flows

报告人：寿凌云 讲师（南京师范大学）    

摘要：We investigate the large-time behavior for finite-energy weak solutions of Vlasov-Navier-Stokes equations in a two-dimensional torus. We first consider the homogeneous case where the incompressible, viscous fluid coupled with the particles has a constant density, and then study the variable-density case. In both cases, we establish the large-time convergence of the distribution function to the monokinetic state. More precisely,  for incompressible Vlasov-Navier-Stokes equations with finite-energy initial data,  we characterize an algebraic time convergence rate of the global weak solution, which deteriorates as the initial particle distribution increases. If the initial particle distribution is sufficiently small, the convergence rate becomes exponential, improving the work of Han-Kwan et al. (2020) dedicated to the homogeneous, three-dimensional case, where an additional smallness condition on the velocity was required. Furthermore, in the non-homogeneous case, we establish similar stability results, allowing a piecewise constant fluid density with jumps. This work is a joint collaboration with Prof. Raphaël Danchin.    

报告时间：2025年5月14日（周三）下午13：30-14：30

报告地点：教二楼727    

联系人：王越