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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

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
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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.

Table of Contents

  • 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
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