Global existence for the interaction of a Navier-Stokes fluid with a linearly elastic shell

TL;DR

This paper proves the existence of global weak solutions for a fluid-structure interaction problem involving Navier-Stokes fluid and a linearly elastic shell, introducing a novel compactness method potentially useful in free boundary fluid dynamics.

Contribution

It presents a new approach to establish compactness of approximate solutions, enabling proof of global existence without damping in the shell equations.

Findings

Existence of global weak solutions for the coupled system.

Introduction of a new compactness method for fluid-structure problems.

Potential applicability of the method to other free boundary problems.

Abstract

In my PhD thesis I show the existence of global-in-time weak solutions for a Navier-Stokes fluid interacting with a linearly elastic shell of Koiter type. This is achieved by the introduction of a new method for showing the compactness of bounded sequences of approximate weak solutions. This method might be of general interest in the study of fluid dynamical problems involving a free boundary. There is no damping term involved in the shell equations.