$L^p$-theory for a fluid-structure interaction model

TL;DR

This paper develops an $L^p$-theory for a fluid-structure interaction model involving an incompressible fluid and a damped Kirchhoff plate, establishing maximal regularity and strong solutions for small data.

Contribution

It introduces an $L^p$-theory for the coupled fluid-structure system using the Newton polygon approach, proving maximal regularity and existence of strong solutions.

Findings

Maximal regularity in $L^p$-Sobolev spaces for the linearized model.

Existence and uniqueness of strong solutions for the nonlinear system with small data.

Application of the Newton polygon approach to fluid-structure interaction models.

Abstract

We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity in $L^p$-Sobolev spaces for a linearized version. Based on this, we show existence and uniqueness of the strong solution of the nonlinear system for small data.