Global weak solutions for some Oldroyd models

TL;DR

This paper proves the global existence of weak solutions for certain Oldroyd models describing non-Newtonian fluid flows, applicable to smooth bounded and periodic domains, for general initial conditions.

Contribution

It establishes the first global existence results for weak solutions of these Oldroyd models in both bounded and periodic domains with general initial data.

Findings

Global weak solutions exist for Oldroyd models in smooth bounded domains.

Results also apply to periodic boundary conditions.

Solutions are valid for general initial data.

Abstract

We investigate an evolutive system of non-linear partial differential equations derived from Oldroyd models on Non-Newtonian flows. We prove global existence of weak solutions, in the case of a smooth bounded domain, for general initial data. The results hold true for the periodic case.