Regularity for an elastic beam interacting with 2D Navier-Stokes equations

A perfectly elastic beam is situated on top of a fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence, the geometry of the fluid domain is a part of the solution. For this setting we show the existence of a unique strong solution by providing an a-priori estimate on the time-derivative of the coupled solution. The estimate is valid for large initial data satisfying natural regularity assumptions and for all times up to the point of a potential collision.