  We introduce and investigate the wellposedness of two models describing the
self-propelled motion of a "small bio-mimetic swimmer" in the 2D and 3D
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]-[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.
