A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact

TL;DR

This paper proves the global existence of weak solutions for a 3D fluid-structure interaction system involving Navier-Stokes fluid and an elastic plate, ensuring no contact occurs between the plate and the boundary.

Contribution

It establishes a global existence result for weak solutions of the coupled Navier-Stokes-plate system with general initial data, preventing contact between the structure and boundary.

Findings

Existence of global weak solutions under general initial conditions

No contact occurs between the elastic plate and the bottom boundary

The coupled system is well-posed for the considered initial data

Abstract

We consider the three-dimensional fluid-structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible Navier-Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. We show that under a rather general condition on the initial data, there exists a global-in-time weak solution of the system. In particular, there is no contact between the plate and the bottom boundary.