External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid
Glass, Olivier; Kolumban, Jozsef; Sueur, Franck (2020), External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid, Analysis & PDE, 13, 3, p. 651-684. 10.2140/apde.2020.13.651
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Article accepté pour publication ou publiéDate
2020Journal name
Analysis & PDEVolume
13Number
3Publisher
Mathematical Sciences Publishers
Pages
651-684
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Show full item recordAbstract (EN)
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the external boundary. Thanks to an impulsive control strategy we prove that there exists an appropriate boundary condition on the remaining part of the external boundary (allowing some fluid going in and out the domain) such that the immersed rigid body is driven from some given initial position and velocity to some final position and velocity in a given positive time, without touching the external boundary. The controlled part of the external boundary is assumed to have a nonvoid interior and the final position is assumed to be in the same connected component of the set of possible positions as the initial position.Subjects / Keywords
external boundary control; Euler equation; control problem; Fluid-solid interaction; impulsive control; geodesics; coupled ODE- PDE system; fluid mechanicsRelated items
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