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

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.