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On the identification of a single body immersed in a Navier-Stokes fluid

Published online by Cambridge University Press:  01 February 2007

A. DOUBOVA ,
E. FERNÁNDEZ-CARA  and
J. H. ORTEGA
A. DOUBOVA
Affiliation:
Universidad de Sevilla, Dpto. E.D.A.N., Aptdo. 1160, 41080 Sevilla, SPAIN emails: doubova@us.es, cara@us.es
E. FERNÁNDEZ-CARA
Affiliation:
Universidad de Sevilla, Dpto. E.D.A.N., Aptdo. 1160, 41080 Sevilla, SPAIN emails: doubova@us.es, cara@us.es
J. H. ORTEGA
Affiliation:
Universidad del Bío-Bío, Facultad de Ciencias, Dpto. de Ciencias Básicas, Casilla 447, Campus Fernando May, Chillán, Chile and Universidad de Chile, Centro de Modelamiento Matemático UMI 2807 CNRS-UChile, Casilla 170/3, Correo 3, Santiago, Chile email: jortega@dim.uchile.cl
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Abstract

In this work we consider the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Navier-Stokes equations. It is assumed that friction forces are known on a part of the outer boundary. We first prove a uniqueness result. Then, we establish a formula for the observed friction forces, at first order, in terms of the deformation of the rigid body. In some particular situations, this provides a strategy that could be used to compute approximations to the solution of the inverse problem. In the proofs we use unique continuation and regularity results for the Navier-Stokes equations and domain variation techniques.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 1 , February 2007 , pp. 57 - 80
Copyright
Copyright © Cambridge University Press 2007

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