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Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying ℝ 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying ℝ 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Control of underwater vehicles in inviscid fluids

Rodrigo Lecaros, Lionel Rosier (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local controllability...

Controllability of 3D low Reynolds number swimmers

Jérôme Lohéac, Alexandre Munnier (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots for which the inertia effects can be neglected. Our first main contribution is to prove that any such microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid. We show that, in addition, this can be done...

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