Abstract

This paper deals with a dynamical shape control problem. The state equations are the non-cylindrical Navier-Stokes equations with a non-homogenous Dirichlet condition. The goal is to compute a necessary optimality condition for the considered functional (kinetic energy). Our work is based on the "transformation" of the domain functional on a field functional and the consideration of transverse fields in the application of the velocity method. The originality of this approach is the introduction of an extra adjoint equation in relation with the initial transverse field to obtain the final form of the necessary condition

Author information

Contact details are reproduced from the original publication and may be historical.

Raja Dziri

Dép. de Mathématiques, Faculté des Sciences, Université de Tunis, 1060 Tunis, Tunisia
and: Lamsin/Enit, 1060 Tunis, Tunisia

Jean-Paul Zolésio

CNRS-INLN, 1361 Route des Lucioles, 06560 Valbonne, France
and: CMA, Ecole des Mines de Paris, 06902 Sophia Antipolis Cedex, France
and: INRIA, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France

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Suggested citation

R. Dziri, J.-P. Zolésio. “Dynamical Shape Control in Non-Cylindrical Navier-Stokes Equations.” Journal of Convex Analysis 6 (1999), No. 2, 293–318. https://doi.org/10.68381/jca06017

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Published by Heldermann Verlag, 1999. Rights now held by Banach Press LLC.