Global Regularity for some Oldroyd-B type Models

TL;DR

This paper proves global regularity for certain Oldroyd-B type visco-elastic flow models in two dimensions by establishing an L-infinity vorticity bound through a specialized transformation.

Contribution

It introduces a novel transformation leveraging the Oldroyd-B structure to achieve global regularity results for specific visco-elastic flow models.

Findings

Established L-infinity vorticity bounds

Proved global regularity in 2D models

Applied transformation technique to Oldroyd-B systems

Abstract

We investigate some critical models for visco-elastic flows of Oldroyd-B type in dimension two. We use a transformation which exploits the Oldroyd-B structure to prove an L^\infty bound on the vorticity which allows us to prove global regularity for our systems.