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

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.

18 pages

References in corpus (2)

• On the interaction between quasilinear elastodynamics and the Navier-Stokes equations
• Existence of global strong solutions to a beam-fluid interaction system

Cited by in corpus (1)

• Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation