Vanishing center-of-mass limit of the 2D-1D corotational Oldroyd-B polymeric fluid-structure interaction problem

Abstract

We consider the Oldroyd-B model for a two-dimensional dilute corotational polymer fluid with center-of-mass diffusion that is interacting with a one-dimensional viscoelastic shell. We show that any family of strong solutions of the system described above that is parametrized by the center-of-mass diffusion coefficient converges, as the coefficient goes to zero, to a weak solution of a corotational polymer fluid-structure interaction system without center-of-mass diffusion but with essentially bounded polymer number density and extra stress tensor. As a consequence, we also obtain a weak-strong uniqueness result that says that the weak solution of the latter is unique in the class of the strong solution of the former as the center-of-mass diffusion vanishes.