Abstract
In this note we announce a number of analytical and numerical results related to the motion of a system S constituted by a rigid body with a cavity that is completely filled with a Navier–Stokes liquid, and that moves in absence of external forces (inertial motions). Our investigation shows, in particular, that the ultimate motion of S about its center of mass is a permanent rotation, thus proving a longstanding conjecture of N.Ye. Zhukovskii. We also present other interesting features of inertial motions that are emphasized by our numerical tests, but that still lack a rigorous mathematical proof.
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