Gevrey Regularity for a Fluid-Structure Interaction Model

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.