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Existence for the linearization of a steady state fluid/nonlinear elasticity interaction

Pages: 184 - 197, Volume 2011, Issue Special, September 2011      doi:10.3934/proc.2011.2011.184

 
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Lorena Bociu - NC State University, Department of Mathematics, 3236 SAS Hall, Raleigh, NC 27695-8205, United States (email)
Jean-Paul Zol├ęsio - CNRS-INLN, 1361 Routes des Lucioles, Sophia Antipolis, F-06560 Valbonne, France (email)

Abstract: A linearized steady state three-dimensional fluid-structure interaction is considered and its solvability is studied. The linearization (obtained in a previous work by these authors) that we deal with has new features, including the presence of the curvature terms on the common interface. These new extra terms, coming from the geometrical aspect of the problem, are critical for a correct physical interpretation of the fluid/structure coupling. We prove that the linearization has unique solution.

Keywords:  Nonlinear Elasticity, Navier-Stokes, Viscous Fluid, Linearization, Coupled System, Existence
Mathematics Subject Classification:  Primary: 76D03, 35Q30, 35Q35

Received: August 2010;      Revised: July 2011;      Available Online: October 2011.