A free discontinuity approach to optimal profiles in Stokes flows
Dorin Bucur
Université de Savoie Mont Blanc, Le Bourget-Du-Lac, FranceAntonin Chambolle
Université de Paris-Dauphine PSL, Paris, France; INRIA Paris, FranceAlessandro Giacomini
Università degli Studi di Brescia, ItalyMickaël Nahon
Université Grenoble Alpes, France
Abstract
In this paper we study obstacles immersed 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 . 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 (). In dimension two, we prove that the solution is classical.
Cite this article
Dorin Bucur, Antonin Chambolle, Alessandro Giacomini, Mickaël Nahon, A free discontinuity approach to optimal profiles in Stokes flows. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first
DOI 10.4171/AIHPC/111