Approximate controllability of linearized shape-dependent operators for flow problems

¹ Fraunhofer ITWM, Transport Processes, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany.
christian.leithaeuser@itwm.fraunhofer.de
² TU Kaiserslautern, Department of Mathematics, Gottlieb-Daimler-Straße, 67663 Kaiserslautern, Germany.
³ Fraunhofer ITWM, Transport Processes, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany.

Received: 14 October 2014
Revised: 27 October 2015
Accepted: 18 February 2016

Abstract

We study the controllability of linearized shape-dependent operators for flow problems. The first operator is a mapping from the shape of the computational domain to the tangential wall velocity of the potential flow problem and the second operator maps to the wall shear stress of the Stokes problem. We derive linearizations of these operators, provide their well-posedness and finally show approximate controllability. The controllability of the linearization shows in what directions the observable can be changed by applying infinitesimal shape deformations.