Three-dimensional nonsimple viscous liquids dragged by one-dimensional immersed bodies

We model the interaction of one-dimensional moving structures with a surrounding three-dimensional fluid, physically close to a Newtonian liquid. The interaction is the adherence of the fluid to the immersed structures, which drag it while moving as rigid bodies. To get solutions of the dynamical problem, we need a model of viscous fluid slightly more general than the Newtonian one, in which the Cauchy stress tensor depends upon higher-order derivatives of the velocity field. Assuming reasonable hypotheses on the motion of the one-dimensional rigid bodies, existence and uniqueness of the solution for the dynamical problem can be proved.