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We consider the motion of a rigid body immersed in an incompressible perfectfluid which occupies a three-dimensional bounded domain. For such a system theCauchy problem is well-posed locally in time if the initial velocity of thefluid is in the Holder space C^{1,r}. In this paper we prove that thesmoothness of the motion of the rigid body may be only limited by thesmoothness of the boundaries (of the body and of the domain). In particular foranalytic boundaries the motion of the rigid body is analytic (till theclassical solution exists and till the solid does not hit the boundary).Moreover in this case this motion depends smoothly on the initial data.

Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid