Well-posedness and applications of classical elastohydrodynamics for a swimming filament

Abstract We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in R 3 . The hydrodynamics are described by resistive force theory, and the fibre elasticity is governed Euler–Bernoulli beam theory. Our aim twofold: (1) Serve as starting point for developing mathematical analysis elastohydrodynamics, particularly analytical treatment inextensibility constraint, (2) As application, prove conditions on internal forcing that allow free-ended to swim. swimming speed supplemented with numerical optimization forcing, well novel method simulating swimmer.