Abstract
AbstractConvergence 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
Reference27 articles.
1. Allaire, G.: Homogenization of the Navier–Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes. Arch. Ration. Mech. Anal. 113(3), 209–259 (1991)
2. Allaire, G.: Homogenization of the Navier–Stokes equations in open sets perforated with tiny holes II: non-critical sizes of the holes for a volume distribution and a surface distribution of holes. Arch. Ration. Mech. Anal. 113(3), 261–298 (1991)
3. Bernard, E., Desvillettes, L., Golse, F., Ricci, V.: A derivation of the Vlasov-Navier-Stokes model for aerosol flows from kinetic theory. Communications in Mathematical Sciences 15(6), 1703–1741 (2017)
4. Billingsley, P.: Convergence of Probability Measures. Wiley, Hoboken (2013)
5. Boudin, L., Desvillettes, L., Grandmont, C., Moussa, A.: Global existence of solutions for the coupled Vlasov and Navier–Stokes equations. Differ. Integr. Equ. 22(11/12), 1247–1271 (2009)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献