2014/05/26 by Giovanni P. Galdi, Giusy Mazzone, Galdi, Giovanni P. +3
Engineering · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Astro and Planetary Science #Cosmology and Gravitation Theories #FOS: Mathematics #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.1405.6596
openalex publication_date 2014/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study inertial motions of the coupled system, S, constituted by a rigid\nbody containing a cavity that is completely filled with a viscous liquid. We\nshow that for data of arbitrary size (initial kinetic energy and total angular\nmomentum) every weak solution (a la Leray-Hopf) converges, as time goes to\ninfinity, to a uniform rotation, thus proving a famous "conjecture" of\nZhukovskii. Moreover we show that, in a wide range of initial data, this\nrotation must occur along the central axis of inertia of S that has the largest\nmoment of inertia. Furthermore, necessary and sufficient conditions for the\nrigorous nonlinear stability of permanent rotations are provided, which improve\nand/or generalize results previously given by other authors under different\ntypes of approximation of the original equations and/or suitable symmetry\nassumptions on the shape of the cavity. Finally, we present a number of results\nobtained by a targeted numerical simulation that, on the one hand, complement\nthe analytical findings, whereas, on the other hand, point out new features\nthat the analysis is yet not able to catch, and, as such, lay the foundation\nfor interesting and challenging future investigation.\n