# American Institute of Mathematical Sciences

May  2003, 9(3): 633-650. doi: 10.3934/dcds.2003.9.633

## Analysis of a linear fluid-structure interaction problem

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

Received  March 2002 Revised  December 2002 Published  February 2003

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.
Citation: Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633
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