Stability of Permanent Rotations and Long-Time Behavior of Inertial Motions of a Rigid Body with an Interior Liquid-Filled Cavity

作者: G. P. Galdi

DOI: 10.1007/978-3-319-60282-0_4

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摘要: A rigid body, with an interior cavity entirely filled a Navier-Stokes liquid, moves in absence of external torques relative to the center mass coupled system body-liquid (inertial motions). The only steady-state motions allowed are then those where system, as whole rotates uniformly around one central axes inertia (permanent rotations). Objective this article is twofold. On hand, we provide sufficient conditions for asymptotic, exponential stability permanent rotations, well their instability. other study asymptotic behavior generic motion class weak solutions and show that there exists time t0 after all such must decay exponentially fast rotation. This result provides full rigorous explanation Zhukovsky’s conjecture, explains, likewise, interesting phenomena observed both lab numerical experiments.