Controllability and kinetic limit of spherical particles immersed in a viscous fluid

TL;DR

This paper investigates the controllability of spherical particles in viscous fluids and explores their kinetic limit as particle numbers grow, using geometric control theory and Boltzmann-type models.

Contribution

It introduces a combined approach using geometric control theory and kinetic modeling to analyze controllability and limits of particle systems in viscous fluids.

Findings

Controllability established for systems with one active and up to two passive particles.

Derivation of Boltzmann-type equations for large particle systems.

Insights into the kinetic behavior as particle number diverges.

Abstract

This paper deals with systems of spherical particles immersed in a viscous fluid. Two aspects are studied, namely the controllability of such systems, with particular attention to the case of one active particle and either one or two passive ones, and the kinetic limit of such systems as the number of particles diverges. The former issue is tackled in the framework of geometric control theory, whereas the latter resorts to Boltzmann-type formulations of the system of interacting particles.