Mean-Field Limit Derivation of a Monokinetic Spray Model with Gyroscopic Effects

TL;DR

This paper derives a two-dimensional spray model with gyroscopic effects as a mean-field limit of fluid-particle interactions, proving existence, uniqueness, and the mean-field convergence in the monokinetic regime with Coulomb interactions.

Contribution

It introduces a new derivation of the spray model with gyroscopic effects and extends the mean-field limit proof to Coulomb interactions in the monokinetic setting.

Findings

Established local existence and uniqueness of strong solutions.

Proved the mean-field limit convergence for Coulomb interactions.

Extended previous models to include gyroscopic effects.

Abstract

In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been studied by Moussa and Sueur (Asymptotic Anal., 2013), in particular the mean-field limit was established in the case of $W^{1,\infty}$ interactions. First we prove the local in time existence and uniqueness of strong solutions of a monokinetic version of the model with a fixed point method. Then we adapt the proof of Duerinckx and Serfaty (Duke Math. J., 2020) to establish the mean-field limit to the spray model in the monokinetic regime in the case of Coulomb interactions.