Remarks on the Blowup Criteria for Oldroyd Models

TL;DR

This paper introduces a simplified method to improve the blowup criterion for Oldroyd viscoelastic models in two dimensions, making the analysis more accessible and adaptable to similar problems.

Contribution

A new, easier approach to prove and enhance the Chemin-Masmoudi blowup criterion for Oldroyd models, avoiding complex losing a priori estimates.

Findings

Improved blowup criterion for Oldroyd models in 2D.

Simplified proof technique for viscoelastic systems.

Potential applicability to other PDE problems.

Abstract

We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in \cite{CM} in two space dimensions. Our method is much easier than the one based on the well-known \textit{losing a priori estimate} and is expected to be easily adopted to other problems involving the losing \textit{a priori} estimate.