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

Abstract

We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a threedimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the H¨older space C1,r. In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic (till the classical solution exists and till the solid does not hit the boundary). Moreover in this case this motion depends smoothly on the initial data.