# Well-posedness of strong solutions for the Vlasov equation coupled to non-Newtonian fluids in dimension three

## TL;DR

This paper proves local and global well-posedness of strong solutions for a coupled Vlasov and non-Newtonian fluid system in three dimensions, under certain initial data conditions.

## Contribution

It establishes the existence, uniqueness, and regularity of solutions for the coupled system, including global solutions for small initial data.

## Key findings

- Local well-posedness of strong solutions
- Global existence for small initial data
- Conditions for regularity and uniqueness

## Abstract

We consider the Cauchy problem for coupled system of Vlasov and non-Newtonian fluid equations. We establish local well--posedness of the strong solutions, provided that the initial data are regular enough. Global existence of unique strong solutions for any given time interval is shown as well if the initial data are sufficiently small.