Global existence results for Oldroyd-B Fluids in exterior domains: The case of non-small coupling parameters

TL;DR

This paper proves the global existence and uniqueness of solutions for Oldroyd-B fluid equations in exterior domains under small initial data conditions, regardless of the size of the coupling parameter.

Contribution

It establishes the first global existence results for Oldroyd-B fluids in exterior domains without requiring the coupling parameter to be small.

Findings

Unique global solutions exist for small initial data.

Solution existence is independent of the coupling constant size.

Results apply to exterior domain geometries.

Abstract

Consider the set of equations describing Oldroyd-B fluids in an exterior domain. It is shown that this set of equations admits a unique, global solution in a certain function space provided the initial data, but not necessarily the coupling constant, is small enough.