Well-posedness of 2-D and 3-D swimming models in incompressible fluids governed by Navier–Stokes equations

We introduce and investigate the wellposedness of two models describing the self-propelled motion of a “small bio-mimetic swimmer” in the 2-D and 3-D incompressible fluids modeled by the Navier–Stokes equations. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by the rotational and elastic forces. The swimmer employs the change of its shape, inflicted by respective explicit internal forces, as the means for self-propulsion in a surrounding medium. Similar models were previously investigated in [15], [16], [17], [18] and [19] where the fluid was modeled by the liner nonstationary Stokes equations. Such models are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids and air.