Equilibrium Configurations and their Uniqueness in a Fluid-Solid Interaction Problem
Analysis of PDEs
2025-12-25 v1
Abstract
We demonstrate existence in the ``large" and uniqueness in the ``small" of equilibrium configurations for the coupled system consisting of a Navier-Stokes fluid interacting with a rigid body subjected to spring forces and restoring moments. The driving mechanism is a uniform, given velocity field of the fluid at large spatial distances from the body. The main difficulty in the proof of the above properties arises from the fact that the body can rotate around a given axis, which produces a highly nonlinear problem.
Cite
@article{arxiv.2512.21130,
title = {Equilibrium Configurations and their Uniqueness in a Fluid-Solid Interaction Problem},
author = {D. Bonheure and G. P. Galdi and C. Patriarca},
journal= {arXiv preprint arXiv:2512.21130},
year = {2025}
}