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

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.