Dynamical Shape Control in Non-cylindrical Navier-Stokes Equations

Creators: Dziri, Raja; Zolésio, Jean-Paul

Others:: Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] (LR-LAMSIN-ENIT) ; Ecole Nationale d'Ingénieurs de Tunis (ENIT) ; Université de Tunis El Manar (UTM)-Université de Tunis El Manar (UTM); Institut Non Linéaire de Nice Sophia-Antipolis (INLN) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS); Centre de Mathématiques Appliquées (CMA) ; Mines Paris - PSL (École nationale supérieure des mines de Paris) ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)

Description

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.

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Article disponible sur le site de l'éditeur : http://www.heldermann.de/JCA/JCA06/JCA062/jca06017.htm

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Dynamical Shape Control in Non-cylindrical Navier-Stokes Equations

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