A boundary control problem for the steady self-propelled motion of a rigid body in a Navier-Stokes fluid

Abstract : We study the self-propelled motions of a rigid body immersed in a viscous incompressible fluid which fills the exterior domain of the rigid body. The mechanism used by the body to reach the desired motion is modeled through a distribution of velocities at its boundary. The fluid motion is modeled by the stationary Navier-Stokes system. These equations are coupled with two relations for the balance of forces and torques. We prove that there exists a control allowing the rigid body to move with a prescribed rigid velocity provided the velocity is small enough. We also show that since the net force exerted by the fluid to the rigid body vanishes, we have a better summability of the fluid velocity than the classical summability result for the solutions of the stationary Navier-Stokes system in exterior domains.
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Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2017
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Toshiaki Hishida, Ana Leonor Silvestre, Takéo Takahashi. A boundary control problem for the steady self-propelled motion of a rigid body in a Navier-Stokes fluid. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2017. <hal-01205210>

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