Nonlocal Stokes-Vlasov system: Existence and deterministic homogenization results

TL;DR

This paper proves the existence of solutions and analyzes the homogenization of a coupled nonlocal Stokes and Vlasov system, with applications to various deterministic settings, advancing understanding of fluid-particle interactions.

Contribution

It establishes the existence of global weak solutions without high-order moment assumptions and applies sigma-convergence to study homogenization in diverse deterministic frameworks.

Findings

Existence of global weak solutions in 2D and 3D.

Homogenization results in periodic, almost-periodic, and weakly almost-periodic settings.

Physical applications demonstrating the homogenization process.

Abstract

Our work deals with the systematic study of the coupling between the nonlocal Stokes system and the Vlasov equation. The coupling is due to a drag force generated by the fluid-particles interaction. We establish the existence of global weak solutions for the nonlocal Stokes-Vlasov system in dimensions two and three without resorting to assumptions on higher-order velocity moments of the initial distribution of particles. We then study by the means of the sigma-convergence method, the asymptotic behavior in the general deterministic framework, of the sequence of solutions to the nonlocal Stokes-Vlasov system. In guise of illustration, we provide several physical applications of the homogenization result including periodic, almost-periodic and weakly almost-periodic settings.