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arXiv · 2308.04809

Existence of a local strong solution to the beam-polymeric fluid interaction system

Dominic Breit·Prince Romeo Mensah
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Abstract

We construct a unique local strong solution to the finitely extensible nonlinear elastic (FENE) dumbbell model of Warner-type for an incompressible polymer fluid (described by the Navier-Stokes-Fokker-Planck equations) interacting with a flexible elastic shell. The latter occupies the flexible boundary of the polymer fluid domain and is modeled by a beam equation coupled through kinematic boundary conditions and the balance of forces. In the 2D case for the co-rotational Fokker-Planck model we obtain global-in-time strong solutions. A main step in our approach is the proof of local well-posedness for just the solvent-structure system in higher-order topologies which is of independent interest. Different from most of the previous results in the literature, the reference spatial domain is an arbitrary smooth subset of $\mathbb{R}^3$, rather than a flat one. That is, we cover viscoelastic shells rather than elastic plates. Our result also supplements the existing literature on the Navier-Stokes-Fokker-Planck equations posed on a fixed bounded domain.

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Dominic Breit, Prince Romeo Mensah. 2023-08-09. Existence of a local strong solution to the beam-polymeric fluid interaction system. https://arxiv.org/abs/2308.04809

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