An elementary proof of uniqueness of the particle trajectories for solutions of a class of shear-thinning non-Newtonian 2D fluids

TL;DR

This paper establishes the uniqueness of particle trajectories in certain 2D shear-thinning non-Newtonian fluids by proving regularity results and applying existing theorems, providing a simplified proof approach.

Contribution

It offers an elementary proof of trajectory uniqueness for a class of non-Newtonian fluids, enhancing understanding of fluid behavior with less complex methods.

Findings

Proved regularity results for 2D shear-thinning fluids

Established uniqueness of particle trajectories using these results

Simplified the proof process compared to previous methods

Abstract

We prove some regularity results for a class of two dimensional non-Newtonian fluids. By applying results from [Dashti and Robinson, Nonlinearity, 22 (2009), 735-746] we can then show uniqueness of particle trajectories.