Strong solution for polymeric fluid-structure interaction with small initial acceleration

Prince Romeo Mensah

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arXiv · 2510.13753

Strong solution for polymeric fluid-structure interaction with small initial acceleration

Prince Romeo Mensah

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Abstract

We consider the problem of a 3D-3D-2D mutually coupled solute-solvent-structure three-states system. This describes the interaction of a flexible structure with a polymeric fluid of classical Oldroyd-B type without centre-of-mass diffusion. We construct a unique higher-order regularity notion of a strong solution for the system by decoupling the solute from the solvent-structure subsystem, solving the decoupled system individually, and gluing the solutions through a fixed-point argument. As a requirement for the construction, we rely on a maximal regularity result for the Stokes problem on moving domains with non-trivial boundary conditions; a result that is also of independent interest.

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Prince Romeo Mensah. 2025-10-15. Strong solution for polymeric fluid-structure interaction with small initial acceleration. https://arxiv.org/abs/2510.13753

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