Inertial motions of a rigid body with a cavity filled with a viscous liquid

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