Mathematical analysis of a one-dimensional model for an aging fluid

TL;DR

This paper provides a rigorous mathematical analysis of a PDE system modeling aging fluids, establishing well-posedness and examining the long-term behavior of solutions in suitable functional spaces.

Contribution

It introduces a new mathematical framework for analyzing aging fluids, proving well-posedness and exploring asymptotic dynamics of the solutions.

Findings

Proved well-posedness of the PDE system

Analyzed the long-time behavior of solutions

Established functional space regularity results

Abstract

We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behaviour of the solutions.