Geodesic
On the Problem of Evolution of an Isolated Liquid Mass
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 3, Tome 3 (2003), pp. 43-62

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The paper is concerned with the problem of stability of equilibrium figures of a uniformly rotating, viscous, incompressible, self-gravitating liquid subjected to capillary forces at the boundary. It is shown that a rotationally symmetric equilibrium figure $F$ is exponentially stable if the functional $G$ defined on the set of domains $\Omega$ close to $F$ and satisfying the conditions of volume invariance ($|\Omega|=|F|$) and the barycenter position attains its minimum for $\Omega=F$. The proof is based on the direct analysis of the corresponding evolution problem with initial data close to the regime of a rigid rotation. 
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     author = {V. A. Solonnikov},
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V. A. Solonnikov. On the Problem of Evolution of an Isolated Liquid Mass. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 3, Tome 3 (2003), pp. 43-62. http://geodesic.mathdoc.fr/item/CMFD_2003_3_a2/