High Reynolds number and high Weissenberg number Oldroyd-B model with dissipation

TL;DR

This paper proves global well-posedness for an incompressible Oldroyd-B model with fractional wave-number dissipation, uniformly across solvent Reynolds numbers, advancing understanding of high Reynolds and Weissenberg number flows.

Contribution

It establishes a small data global well-posedness result for the Oldroyd-B model with fractional dissipation, uniform in Reynolds number, which was previously unresolved.

Findings

Global well-posedness for small data

Uniformity in solvent Reynolds numbers

Fractional wave-number dissipation suffices

Abstract

We give a small data global well-posedness result for an incompressible Oldroyd-B model with wave number dissipation in the equation of stress tensor. The result is uniform in solvent Reynolds numbers, and requires only fractional wave-number dependent dissipation $(-\Delta)^{\beta}$, $\beta \ge \frac{1}{2}$ in the added stress.