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Contactless rebound of elastic bodies in a viscous incompressible fluid

Published online by Cambridge University Press:  24 May 2022

G. Gravina
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic Department of Mathematics, Temple University, Philadelphia, PA 19122, USA
S. Schwarzacher*
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
O. Souček
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
K. Tůma
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Prague, Czech Republic
Email address for correspondence:


In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, where it is now well established that collisions cannot occur in finite time under certain assumptions. In a simplified framework, we provide conditions which allow us to prove that rebound is possible even in the absence of a topological contact. Our results lead to the conjecture that a qualitative change in the shape of the solid is necessary to obtain a physically meaningful rebound in fluids. We support the conjecture by comparing numerical simulations performed for the reduced model with finite element solutions obtained for corresponding well-established partial differential equation systems describing elastic solids interacting with incompressible fluids.

JFM Papers
© The Author(s), 2022. Published by Cambridge University Press

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