Convergence of a system of particles, interacting with a fluid, to Navier–Stokes–Vlasov–Fokker–Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is proved to converge to the Vlasov–Fokker–Planck component of the system and the velocity of the fluid coupled with the particles converges in the uniform topology to the the Navier–Stokes component. A new uniqueness result for the PDE system is added.

中文翻译：

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Navier–Stokes–Vlasov–Fokker–Planck系统作为流体中颗粒的比例极限

研究了与流体相互作用的粒子系统在Navier–Stokes–Vlasov–Fokker–Planck系统中的收敛性。斯托克斯拖曳力描述了颗粒与流体之间的相互作用。粒子的经验度量被证明收敛到系统的Vlasov–Fokker–Planck分量，并且与粒子耦合的流体速度以统一的拓扑收敛到Navier–Stokes分量。为PDE系统添加了新的唯一性结果。