Existence of solutions for the equations

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Abstract
We introduce a concept of weak solution for a boundary value problem modelling the interactive motion of a coupled system consisting in a rigid body immersed in a viscous fluid. The fluid, and the solid are contained in a fixed open bounded set of R3. The motion of the fluid is governed by the incompresible Navier-Stokes equations and the standard conservation's laws of linear, and angular momentum rules the dynamics of the rigid body. The time variation of the fluid's domain (due to the motion of the rigid body) is not known apriori, so we deal with a free boundary value problem. Our main theorem asserts the existence of at least one weak solution for this problem. The result is global in time provided that the rigid body does not touch the boundary

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