Gevrey regularity for a system coupling the Navier-Stokes system with a beam: the non-flat case

TL;DR

This paper proves the existence of strong solutions for a 2D viscous incompressible fluid interacting with a boundary beam, demonstrating that the associated semigroup is of Gevrey class, thus extending previous small-deformation results.

Contribution

It extends prior work by establishing strong solutions without the small initial deformation assumption, focusing on the Gevrey regularity of the linearized system.

Findings

Existence of strong solutions for the fluid-beam interaction system.

The semigroup associated with the linearized system is of Gevrey class.

Extension of previous results to non-small initial deformations.

Abstract

We consider a bi-dimensional viscous incompressible fluid in interaction with a beam located at its boundary. We show the existence of strong solutions for this fluid-structure interaction system, extending a previous result where we supposed that the initial deformation of the beam was small. The main point of the proof consists in the study of the linearized system and in particular in proving that the corresponding semigroup is of Gevrey class.