Strong solution for polymeric fluid-structure interaction with small initial acceleration
Analysis of PDEs
2025-10-16 v1
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 glueing 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.
Cite
@article{arxiv.2510.13753,
title = {Strong solution for polymeric fluid-structure interaction with small initial acceleration},
author = {Prince Romeo Mensah},
journal= {arXiv preprint arXiv:2510.13753},
year = {2025}
}