Equilibrium Configurations and their Uniqueness in a Fluid-Solid Interaction Problem

TL;DR

This paper proves the existence of equilibrium states in a fluid-solid interaction system with a Navier-Stokes fluid and a rotating rigid body, and establishes their uniqueness under small perturbations, addressing nonlinear rotational effects.

Contribution

It introduces new mathematical results on existence and uniqueness of equilibrium configurations in a complex fluid-solid interaction with rotation.

Findings

Existence of equilibrium configurations in large-scale fluid-solid systems.

Uniqueness of these configurations when perturbations are small.

Handling of nonlinear rotational dynamics in the proof.

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.