Abstract

We consider the motion of several rigid bodies immersed in a two-dimensional incompressible perfect fluid, the whole system occupying a bounded simply connected domain. The external fixed boundary is impermeable except on an open nonempty part where one controls both the normal velocity, allowing some fluid to go in and out of the domain, and the entering vorticity. The motion of the rigid bodies is given by the Newton laws with forces due to the fluid pressure and the fluid motion is described by the incompressible Euler equations. We prove that it is possible to exactly achieve any noncolliding smooth motion of the rigid bodies by the remote action of a controlled normal velocity on the outer boundary which takes the form of state-feedback, with zero entering vorticity. The proof relies on a nonlinear method to solve linear perturbations of nonlinear equations associated with a quadratic operator.

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