Weak and strong solutions for polymeric fluid-structure interaction of Oldroyd-B type

TL;DR

This paper establishes the existence and uniqueness of weak and strong solutions for a complex fluid-structure interaction model involving Oldroyd-B type polymeric fluids and elastic shells, with implications for understanding dilute polymer flows.

Contribution

It proves the global existence of weak and strong solutions for a coupled polymer fluid and elastic shell system, including weak-strong uniqueness, in a two-dimensional setting.

Findings

Existence of weak solutions for the polymeric fluid-structure system.

Existence and uniqueness of strong solutions under certain conditions.

Global solutions are maintained over time without degeneracy.

Abstract

We prove the existence of weak solutions and a unique strong solution to the Oldroyd-B dumbbell model describing the evolution of a two-dimensional dilute polymer fluid interacting with a one-dimensional viscoelastic shell. The polymer fluid consists of a mixture of an incompressible viscous solvent and a solute comprising two massless beads connected by a Hookean spring with center-of-mass diffusion. This solute-solvent mixture then interacts with a flexible structure that evolves in time. An arbitrary nondegenerate reference domain for the polymer fluid is allowed and both solutions exist globally in time provided no future degeneracies occur with the structure deformation. Furthermore, weak-strong uniqueness holds unconditionally.