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arXiv · 2009.14160

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.

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Dominic Breit, Prince Romeo Mensah. 2020-09-29. An incompressible polymer fluid interacting with a Koiter shell. https://doi.org/10.1007/s00332-021-09678-5

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