Gevrey Regularity for a System Coupling the Navier-Stokes System with a Beam: the Non-Flat Case

抄録

We consider a two-dimensional viscous incompressible fluid in interaction with a one-dimensional beam located at its boundary. We show the existence of strong solutions for this fluid-structure interaction system, extending a previous result, where the initial deformation of the beam was assumed to be small. Here our result is valid for any smooth initial deformation (W^7,∞) with no restriction on the size. The main point of the proof consists in the study of the linearized system in a non-cartesian domain and in particular in proving that the corresponding semigroup is of Gevrey class.