Stability of a Simple Solution of Shallow Water Equations on a Rotating Gravitating Sphere

E. V. Mamontov

doi:10.1007/s10958-014-2158-7

Stability of a Simple Solution of Shallow Water Equations on a Rotating Gravitating Sphere

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Abstract

We study the stability of a partial solution to the shallow water equations governing a rotating gravitating sphere. We reduce the problem to searching for eigenvalues of a singular boundary value problem for the system of four ordinary differential equations. We show that the solution is stable under perturbations depending only on the latitude variable. In the general case, a numerical experiment shows that the eigenvalues are purely imaginary, i.e., the solution is stable under arbitrary small perturbations. Bibliography: 3 titles. Illustrations: 1 figure.

Original language	English
Pages (from-to)	551-557
Number of pages	7
Journal	Journal of Mathematical Sciences (United States)
Volume	203
Issue number	4
DOIs	https://doi.org/10.1007/s10958-014-2158-7
State	Published - Dec 2014
Externally published	Yes

Funding

The work was supported by the Russian Foundation for Basic Research (projects No. 11-01-00026-a) and the Federal Agency for Science and Innovation of the Russian Federation (grant No. NSh-6706.2012.1).

Funders	Funder number
Russian Foundation for Basic Research	11-01-00026-a
Federal Agency of Atomic Energy of the Russian Federation

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10.1007/s10958-014-2158-7

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Stability of a Simple Solution of Shallow Water Equations on a Rotating Gravitating Sphere

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