The inertialess limit of particle sedimentation modeled by the Vlasov-Stokes equations

TL;DR

This paper analyzes the limit of particle sedimentation modeled by Vlasov-Stokes equations as particle inertia vanishes, showing convergence to an inertialess system that aligns with homogenized microscopic models.

Contribution

It establishes the rigorous convergence of the Vlasov-Stokes system to an inertialess model as particle inertia approaches zero.

Findings

Proves convergence of particle dynamics to inertialess system.

Connects macroscopic and microscopic inertialess models.

Provides mathematical validation for the inertialess limit.

Abstract

We study the Vlasov-Stokes equations which macroscopically model the sedimentation of a cloud of particles in a fluid, where particle inertia are taken into account but fluid inertia are assumed to be negligible. We consider the limit when the inertia of the particles tends to zero, and obtain convergence of the dynamics to the solution of an associated inertialess system of equations. This system coincides with the model that can be derived as the homogenization limit of the microscopic inertialess dynamics.