We consider the free fall of slender rigid bodies in a viscous incompressible
fluid. We show that the dimensional reduction (DR), performed by substituting
the slender bodies with one-dimensional rigid objects, together with a
hyperviscous regularization (HR) of the Navier--Stokes equation for the
three-dimensional fluid lead to a well-posed fluid-structure interaction
problem. In contrast to what can be achieved within a classical framework, the
hyperviscous term permits a sound definition of the viscous force acting on the
one-dimensional immersed body. Those results show that the DR/HR procedure can
be effectively employed for the mathematical modeling of the free fall problem
in the slender-body limit.Comment: arXiv admin note: substantial text overlap with arXiv:1305.070
