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Sibirskii Zhurnal Industrial'noi Matematiki, 2011, Volume 14, Number 4, Pages 44–49
(Mi sjim696)
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This article is cited in 1 scientific paper (total in 1 paper)
On the stability of the stationary solution to the shallow water equation on a rotating gravitating sphere
E. V. Mamontov Lavrent'ev Institute of Hydrodynamics, Siberian Division of the RAS, Novosibirsk, RUSSIA
Abstract:
We discuss the question of stability of the constant solution to the shallow water equation on a rotating gravitating sphere. The problem reduces to finding eigenvalues in a singular boundary value problem for a system of four first-order ODEs. We show that the eigenvalues are pure imaginary; thus, the solution in question is stable under small perturbations of arbitrary kinds.
Keywords:
shallow water, sphere, eigenvalues, stability.
Received: 16.03.2011
Citation:
E. V. Mamontov, “On the stability of the stationary solution to the shallow water equation on a rotating gravitating sphere”, Sib. Zh. Ind. Mat., 14:4 (2011), 44–49
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https://www.mathnet.ru/eng/sjim696 https://www.mathnet.ru/eng/sjim/v14/i4/p44
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Abstract page: | 237 | Full-text PDF : | 84 | References: | 36 | First page: | 1 |
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