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.
Giusteri, G. G., Marzocchi, A., Musesti, A., Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids, <<DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.>>, 2014; 19 (7): 2145-2157. [doi:10.3934/dcdsb.2014.19.2145] [http://hdl.handle.net/10807/59663]