Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Analysis of a linear fluid-structure interaction problem

Pages: 633 - 650, Volume 9, Issue 3, May 2003      doi:10.3934/dcds.2003.9.633

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Qiang Du - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA, United States (email)
M. D. Gunzburger - School of Computational Science and Information Technology, Florida State University; Tallahassee FL 32306, United States (email)
L. S. Hou - Department of Mathematics, Iowa State University; Ames, IA 50011, United States (email)
J. Lee - Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, United States (email)

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.

Keywords:  Fluid-structure interaction, incompressible fluid, linear elasticity.
Mathematics Subject Classification:  35Q30, 76D07, 73C02, 73K12.

Received: March 2002;      Revised: December 2002;      Available Online: February 2003.