An Incompressible Polymer Fluid Interacting with a Koiter Shell

Dominic Breit, Prince Romeo Mensah

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Abstract

We study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.
Original languageEnglish
Article number25
JournalJournal of Nonlinear Science
Volume31
Issue number1
Early online date12 Feb 2021
DOIs
Publication statusPublished - Feb 2021

Keywords

  • FENE model
  • Fluid-structure interaction
  • Incompressible Navier–Stokes–Fokker–Planck system
  • Koiter shell

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Applied Mathematics

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