# American Institute of Mathematical Sciences

September  2014, 19(7): 2145-2157. doi: 10.3934/dcdsb.2014.19.2145

## Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids

 1 Dipartimento di Matematica e Fisica "N. Tartaglia", Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy, Italy, Italy

Received  May 2013 Revised  March 2014 Published  August 2014

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.
Citation: Giulio G. Giusteri, Alfredo Marzocchi, Alessandro Musesti. Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2145-2157. doi: 10.3934/dcdsb.2014.19.2145
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