The Navier–Stokes–Vlasov–Fokker–Planck System as a Scaling Limit of Particles in a Fluid
Franco Flandoli, Marta Leocata, Cristiano Ricci
2021IRIS - Institutional Research Information System (Libera Università Internazionale degli Studi Sociali Guido Carli)12 citationsDOIOpen Access PDF
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.
Topics & Concepts
Fokker–Planck equationPhysicsUniquenessDragStokes numberClassical mechanicsScalingConvergence (economics)Limit (mathematics)Navier–Stokes equationsMathematical analysisMechanicsTurbulenceMathematicsDifferential equationQuantum mechanicsCompressibilityGeometryReynolds numberEconomicsEconomic growthGas Dynamics and Kinetic TheoryAdvanced Thermodynamics and Statistical MechanicsPhase Equilibria and Thermodynamics