Mathematical analysis of the stationary Oldroyd model with diffusive stress

TL;DR

This paper provides a rigorous mathematical analysis of the stationary Oldroyd model with diffusive stress, establishing existence and uniqueness of solutions under certain conditions, and extending results to strong solutions with more regular data.

Contribution

It introduces new existence and uniqueness results for the stationary Oldroyd model with diffusive stress, including relaxed conditions in the corotational case and strong solutions with higher regularity.

Findings

Existence and uniqueness of weak solutions under small data or parameters

Relaxed conditions for the corotational model

Existence of strong solutions with additional regularity

Abstract

We present the mathematical analysis of the stationary Oldroyd model with diffusive stress: existence and uniqueness of weak solutions is shown if the source terms are small enough or if the Reynolds and Weissenberg numbers are small enough. Besides, in the corotational model, this condition on the data can be relaxed for the existence result. Finally, strong solutions are obtained with additional regularity on the data.