Gevrey Regularity for a Fluid-Structure Interaction Model

TL;DR

This paper proves Gevrey regularity for a fluid-structure interaction model involving a coupled fluid and plate equation, using resolvent estimates and numerical demonstrations of smoothing effects.

Contribution

It establishes Gevrey regularity for a complex fluid-structure interaction semigroup and provides a numerical scheme to empirically verify smoothing properties.

Findings

Gevrey regularity is proven for the semigroup modeling the interaction.

A resolvent estimate is key to establishing regularity.

Numerical examples demonstrate smoothing effects.

Abstract

A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry $\mathcal{O}$. On a portion of the boundary, a fourth order plate equation is coupled with the fluid through pressure and matching velocities. The key to obtaining the conclusion of Gevrey regularity is an appropriate estimation of the resolvent of the associated $C_0$-semigroup operator. Moreover, a numerical scheme and example is provided which empirically demonstrates smoothing of the fluid-structure semigroup.