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A free discontinuity approach to optimal profiles in stokes flows

Bucur, Dorin; Chambolle, Antonin; Giacomini, Alessandro; Nahon, Mickaël (2023), A free discontinuity approach to optimal profiles in stokes flows. https://basepub.dauphine.psl.eu/handle/123456789/24491

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Type
Document de travail / Working paper
Date
2023
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
41
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Author(s)
Bucur, Dorin
Laboratoire de Mathématiques [LAMA]
Chambolle, Antonin cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Giacomini, Alessandro
Dipartimento di Matematica [Universita di Brescia]
Nahon, Mickaël
Max-Planck-Institut für Mathematik in den Naturwissenschaften [MPI-MiS]
Abstract (EN)
In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes of prescribed volume and controlled surface area, taking into account that these shapes may naturally develop geometric features of codimension 1. The existence is carried out in the framework of free discontinuity problems and leads to a relaxed solution in the space of special functions of bounded deformation (SBD). In dimension 2, we prove that the solution is classical.
Subjects / Keywords
Free discontinuity problems; Stokes flow; Navier boundary conditions; Drag