Global weak solutions for an Newtonian Fluid interacting with a Koiter Type Shell under natural boundary conditions

TL;DR

This paper proves the existence of global weak solutions for a coupled fluid-structure system involving an incompressible Newtonian fluid and a linearized Koiter shell, under natural boundary conditions, assuming the shell remains non-self-intersecting.

Contribution

It establishes the existence of weak solutions for fluid-structure interaction with a Koiter shell under natural boundary conditions, a novel result in this setting.

Findings

Weak solutions exist as long as the shell does not self-intersect.

The coupling conditions ensure the continuity of velocities and surface forces.

The analysis covers natural boundary conditions on fixed in- and outflow regions.

Abstract

We consider an viscous, incompressible Newtonian fluid flowing through a thin elastic structure. The motion of the structure is described by the equations of a linearised Koiter shell, whose motion is restricted to transverse displacements. The fluid and the structure are coupled by the continuity of velocities and an equilibrium of surface forces on the interface between fluid and structure. On a fixed in- and outflow region we prescribe natural boundary conditions. We show that weak solutions exist as long as the shell does not self-intersect.