论文标题
关于不可压缩流中带电颗粒的动力学：从动流体到流体流体模型
On the dynamics of charged particles in an incompressible flow: from kinetic-fluid to fluid-fluid models
论文作者
论文摘要
在本文中，我们对与不可压缩粘性流相互作用的带电颗粒的动力学感兴趣。更确切地说，我们考虑了Vlasov-Poisson或Vlasov-Poisson-Fokker-Planck方程，并通过阻力力加上不可压缩的Navier-Stokes系统。对于提出的动力流体模型，我们研究了对应于强局部比对和扩散力的渐近状态。在对初始数据的合适假设下，我们严格地得出了一个耦合的等温/无压力欧拉 - 偏见系统和不可压缩的Navier-Stokes System（简而言之，EPNS系统）。对于这种流体动力学极限，我们将调制的动能估计与相对熵方法和有界的Lipschitz距离一起使用。我们还为等温/无压力EPNS系统构建了全球时间强的可溶性。特别是，这种全球时间溶解度给出了一直以来一直保持流体动力极限的估计值。
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible Navier-Stokes system through the drag force. For the proposed kinetic-fluid model, we study the asymptotic regime corresponding to strong local alignment and diffusion forces. Under suitable assumptions on the initial data, we rigorously derive a coupled isothermal/pressureless Euler-Poisson system and incompressible Navier-Stokes system(in short, EPNS system). For this hydrodynamic limit, we employ the modulated kinetic energy estimate together with the relative entropy method and the bounded Lipschitz distance. We also construct a global-in-time strong solvability for the isothermal/pressureless EPNS system. In particular, this global-in-time solvability gives the estimates of hydrodynamic limit hold for all time.
