A boundary control problem for the steady self-propelled motion of a rigid body in a Navier–Stokes fluid
Ana Leonor Silvestre
CEMAT and Department of Mathematics, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalTakéo Takahashi
Inria Nancy Grand-Est, 615 rue du Jardin Botanique, 54600 Villers-lès-Nancy, France; Institut Élie Cartan, UMR CNRS 7502, Université de Lorraine, Boulevard des Aiguillettes, B.P. 70239, 54506 Vandoeuvre-lès-Nancy, Cedex, FranceToshiaki Hishida
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
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Abstract
Consider a rigid body immersed in an infinitely extended Navier–Stokes fluid. We are interested in self-propelled motions of in the steady state regime of the system rigid body-fluid, assuming that the mechanism used by the body to reach such a motion is modeled through a distribution of velocities on . If the velocity of is given, can we find that generates ? We show that this can be solved as a control problem in which is a six-dimensional control such that either , an arbitrary nonempty open subset of , or . We also show that one of the self-propelled conditions implies a better summability of the fluid velocity.
Cite this article
Ana Leonor Silvestre, Takéo Takahashi, Toshiaki Hishida, A boundary control problem for the steady self-propelled motion of a rigid body in a Navier–Stokes fluid. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 6, pp. 1507–1541
DOI 10.1016/J.ANIHPC.2016.11.003