  A new slender-body theory for viscous flow, based on the concepts of
dimensional reduction and hyperviscous regularization, is presented. The
geometry of flat, elongated, or point-like rigid bodies immersed in a viscous
fluid is approximated by lower-dimensional objects, and a hyperviscous term is
added to the flow equation. The hyperviscosity is given by the product of the
ordinary viscosity with the square of a length that is shown to play the role
of effective thickness of any lower-dimensional object. Explicit solutions of
simple problems illustrate how the proposed method is able to represent with
good approximation both the velocity field and the drag forces generated by
rigid motions of the immersed bodies, in analogy with classical slender-body
theories. This approach has the potential to open up the way to more effective
computational techniques, since the complexity of the geometry can be
significantly reduced. This, however, is achieved at the expense of involving
higher-order derivatives of the velocity field. Importantly, both the
dimensional reduction and the hyperviscous regularization, combined with
suitable numerical schemes, can be used also in situations where inertia is not
negligible.
