European Journal of Applied Mathematics

Table of Contents - February 2007 - Volume 18, Issue 01  

Papers

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

A. DOUBOVAa1, E. FERNÁNDEZ-CARAa1 and J. H. ORTEGAa2

a1 Universidad de Sevilla, Dpto. E.D.A.N., Aptdo. 1160, 41080 Sevilla, SPAIN emails: doubova@us.es, cara@us.es

a2 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

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.

(Received November 16 2005)

(Revised July 20 2006)

(Online publication February 09 2007)