二维非齐次不可压缩Navier-Stokes/Vlasov-Fokker-Planck方程组的渐近分析

Asymptotic analysis for 2D inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations

研究了二维空间中非齐次不可压缩Navier-Stokes/Vlasov-Fokker-Planck方程组的渐近分析,此模型用于塑造流体-粒子的相互作用.运用紧性方法得到ρ~ε,u~ε的强收敛,最终得到由关于粒子宏观密度的对流-扩散方程及不可压缩Navier-Stokes方程组成的极限方程组.本文将相关文献的结果推广到非齐次不可压缩的情形.

In this paper,we study the the asymptotic analysis of inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations in two dimensions,which models the interaction of the fluid and particles.We obtain the strong convergence of ",u"by using compactness principle,as a result,we obtain the limit problem,which consists of an advection-diffusion equation for the macroscopic density of the particles and incompressible Navier-Stokes equation.This work extends the previous result to the inhomogeneous incompressiblecase.