Flocking particles in a non-Newtonian shear thickening fluid

TL;DR

This paper establishes the mathematical existence and uniqueness of solutions for a flocking model coupled with a non-Newtonian fluid, advancing understanding of complex fluid-structure interactions in a periodic domain.

Contribution

It proves the existence and uniqueness of strong solutions for a coupled flocking and non-Newtonian fluid model with power-law stress tensor for specific parameters.

Findings

Existence of strong solutions for the coupled model.

Uniqueness of solutions under specified conditions.

Extension of mathematical theory to non-Newtonian fluid-structure interactions.

Abstract

We prove existence and uniqueness of strong solutions to the Cucker--Smale flocking model coupled with an incompressible viscous non-Newtonian fluid, with the stress tensor of a power--law structure for $p\geq\frac{11}{5}$. The coupling is performed through a drag force on a periodic spatial domain $T^3$.