2021-07-29T23:56:07Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000251352021-03-01T13:44:51ZA boundary control problem for the steady self-propelled motion of a rigid body in a Navier–Stokes fluidHishida, ToshiakiSilvestre, Ana LeonorTakahashi, Takeo© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/3-D Navier–Stokes equationsExterior domainRotating bodySelf-propelled motionBoundary controlAsymptotic behaviorConsider a rigid body S⊂R^3 immersed in an infinitely extended Navier–Stokes fluid. We are interested in self-propelled motions of S 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 \nv□ on ∂S. If the velocity V of S is given, can we find \nv□ that generates V? We show that this can be solved as a control problem in which \nv□ is a six-dimensional control such that either \nSuppv□⊂Γ, an arbitrary nonempty open subset of ∂Ω, or \nv□⋅n|∂Ω=0. We also show that one of the self-propelled conditions implies a better summability of the fluid velocity.Elsevier2017-12engjournal articlehttp://hdl.handle.net/2237/27355https://nagoya.repo.nii.ac.jp/records/251350294-1449Annales de l'Institut Henri Poincaré C, Analyse non linéaire34615071541https://nagoya.repo.nii.ac.jp/record/25135/files/thalstt_2016_11_14.pdfapplication/pdf455.8 kB2019-12-01