Steady free fall of one-dimensional bodies in a  hyperviscous fluid at low Reynolds number

Giulio G. Giusteri; Alfredo Marzocchi; Alessandro Musesti

doi:10.3934/eect.2014.3.429

Article Contents

2014, Volume 3, Issue 3: 429-445. Doi: 10.3934/eect.2014.3.429

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Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number

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

Received: April 2013

Revised: January 2014

Published: September 2014

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Abstract

The paper is devoted to the study of the motion of one-dimensional rigid bodies during a free fall in a quasi-Newtonian hyperviscous fluid at low Reynolds number. We show the existence of a steady solution and furnish sufficient conditions on the geometry of the body in order to get purely translational motions. Such conditions are based on a generalized version of the so-called Reciprocal Theorem for fluids.

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Mathematics Subject Classification: Primary: 76D07; Secondary: 35Q35, 35J91.

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