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Contemporary Mathematics. Fundamental Directions, 2003, Volume 3, Pages 43–62
(Mi cmfd15)
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This article is cited in 5 scientific papers (total in 5 papers)
On the Problem of Evolution of an Isolated Liquid Mass
V. A. Solonnikov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
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.
Citation:
V. A. Solonnikov, “On the Problem of Evolution of an Isolated Liquid Mass”, 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, CMFD, 3, MAI, M., 2003, 43–62; Journal of Mathematical Sciences, 124:6 (2004), 5442–5460
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https://www.mathnet.ru/eng/cmfd15 https://www.mathnet.ru/eng/cmfd/v3/p43
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Abstract page: | 302 | Full-text PDF : | 93 | References: | 56 |
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