We consider the free boundary problem for the Navier–Stokes equations governing a nonstationary motion of a layer of a viscous incompressible liquid that covers the surface of a rigid ball rotating around a fixed axis with constant angular velocity ω. The liquid is subject to the gravitation force generated by the mass of the ball. The self-gravitation forces between the liquid particles and capillary forces on the free surface are not taken into account. We consider the problem of stability of the regime of the rigid rotation of the liquid with the same angular velocity and prove that it is stable if |ω| is less than a certain constant. Bibliography: 10 titles.
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Translated from Problems in Mathematical Analysis 39 February, 2009, pp. 91–145.
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Solonnikov, V.A. On the nonstationary motion of a viscous incompressible liquid over a rotating ball. J Math Sci 157, 885–947 (2009). https://doi.org/10.1007/s10958-009-9364-8
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DOI: https://doi.org/10.1007/s10958-009-9364-8