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2003, Volume 9, Issue 3: 633-650. Doi: 10.3934/dcds.2003.9.633

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Analysis of a linear fluid-structure interaction problem

1.
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
2.
School of Computational Science and Information Technology, Florida State University; Tallahassee FL 32306
3.
Department of Mathematics, Iowa State University; Ames, IA 50011
4.
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213

Received: March 2002

Revised: December 2002

Published: May 2003

Abstract / Introduction Related Papers Cited by

Abstract

A time-dependent system modeling the interaction between a Stokes fluid and an elastic structure is studied. A divergence-free weak formulation is introduced which does not involve the fluid pressure field. The existence and uniqueness of a weak solution is proved. Strong energy estimates are derived under additional assumptions on the data. The existence of an $L^2$ integrable pressure field is established after the verification of an inf-sup condition.

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Mathematics Subject Classification: 35Q30, 76D07, 73C02, 73K12.

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