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.
The Navier–Stokes–Vlasov–Fokker–Planck System as a Scaling Limit of Particles in a Fluid / Flandoli, F.; Leocata, Marta; Ricci, Cristiano. - In: JOURNAL OF MATHEMATICAL FLUID MECHANICS. - ISSN 1422-6928. - 23:2(2021), pp. 1-39. [10.1007/s00021-021-00570-6]
The Navier–Stokes–Vlasov–Fokker–Planck System as a Scaling Limit of Particles in a Fluid
Leocata M.;Ricci C.
2021
Abstract
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.
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