A boundary control problem for the steady self-propelled motion of a rigid body in a Navier–Stokes fluid
Annales de l'I.H.P. Analyse non linéaire, Volume 34 (2017) no. 6, pp. 1507-1541.

Consider a rigid body SR3 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 v on S. If the velocity V of S is given, can we find v that generates V? We show that this can be solved as a control problem in which v is a six-dimensional control such that either SuppvΓ, an arbitrary nonempty open subset of ∂Ω, or vn|Ω=0. We also show that one of the self-propelled conditions implies a better summability of the fluid velocity.

DOI: 10.1016/j.anihpc.2016.11.003
Keywords: 3-D Navier–Stokes equations, Exterior domain, Rotating body, Self-propelled motion, Boundary control, Asymptotic behavior
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     title = {A boundary control problem for the steady self-propelled motion of a rigid body in a {Navier{\textendash}Stokes} fluid},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1507--1541},
     publisher = {Elsevier},
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Hishida, Toshiaki; Silvestre, Ana Leonor; Takahashi, Takéo. A boundary control problem for the steady self-propelled motion of a rigid body in a Navier–Stokes fluid. Annales de l'I.H.P. Analyse non linéaire, Volume 34 (2017) no. 6, pp. 1507-1541. doi : 10.1016/j.anihpc.2016.11.003. http://www.numdam.org/articles/10.1016/j.anihpc.2016.11.003/

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