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

Lorena Bociu; Jean-Paul Zolésio

doi:10.3934/proc.2011.2011.184

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2011, Volume 2011: 184-197. Doi: 10.3934/proc.2011.2011.184 open access

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

Lorena Bociu^1, and
Jean-Paul Zolésio^2,

1.
NC State University, Department of Mathematics, 3236 SAS Hall, Raleigh, NC 27695-8205
2.
CNRS-INLN, 1361 Routes des Lucioles, Sophia Antipolis, F-06560 Valbonne

Received: August 2010

Revised: July 2011

Published: August 2017

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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.

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Mathematics Subject Classification: Primary: 76D03, 35Q30, 35Q35.

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