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On the Steady Motion of a Coupled System Solid-Liquid
Josef Bemelmans, Rheinisch-Westf Technische Hochschule-Aachen, Germany, Giovanni P. Galdi, University of Pittsburgh, PA, and Mads Kyed, Technische Universität Darmstadt, Germany
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Memoirs of the American Mathematical Society
2013; 89 pp; softcover
Volume: 226
ISBN-10: 0-8218-8773-4
ISBN-13: 978-0-8218-8773-8
List Price: US$72 Individual Members: US$43.20
Institutional Members: US\$57.60
Order Code: MEMO/226/1060

The authors study the unconstrained (free) motion of an elastic solid $$\mathcal B$$ in a Navier-Stokes liquid $$\mathcal L$$ occupying the whole space outside $$\mathcal B$$, under the assumption that a constant body force $$\mathfrak b$$ is acting on $$\mathcal B$$. More specifically, the authors are interested in the steady motion of the coupled system $$\{\mathcal B,\mathcal L\}$$, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. The authors prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of $$\mathcal B$$ satisfies suitable geometric properties.

• Introduction
• Notation and preliminaries
• Steady free motion: Definition and formulation of the problem
• Main result
• Approximating problem in bounded domains
• Proof of main theorem
• Bodies with symmetry
• Appendix A. Isolated orientation
• Bibliography