  The optimal strategy for a microscopic swimmer to migrate across a linear
shear flow is discussed. The two cases, in which the swimmer is located at
large distance, and in the proximity of a solid wall, are taken into account.
It is shown that migration can be achieved by means of a combination of sailing
through the flow and swimming, where the swimming strokes are induced by the
external flow without need of internal energy sources or external drives. The
structural dynamics required for the swimmer to move in the desired direction
is discussed and two simple models, based respectively on the presence of an
elastic structure, and on an orientation dependent friction, to control the
deformations induced by the external flow, are analyzed. In all cases, the
deformation sequence is a generalization of the tank-treading motion regimes
observed in vesicles in shear flows. Analytic expressions for the migration
velocity as a function of the deformation pattern and amplitude are provided.
The effects of thermal fluctuations on propulsion have been discussed and the
possibility that noise be exploited to overcome the limitations imposed on the
microswimmer by the scallop theorem have been discussed.
