Geodesic
On the stability of the stationary solution to the shallow water equation on a~rotating gravitating sphere
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 44-49.

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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. 
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E. V. Mamontov. On the stability of the stationary solution to the shallow water equation on a~rotating gravitating sphere. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 44-49. http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a4/

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[2] Cherevko A. A., Chupakhin A. P., “Uravneniya melkoi vody na vraschayuscheisya prityagivayuschei sfere. 2: Prostye statsionarnye volny i zvukovye kharakteristiki”, Prikl. mekhanika i tekhn. fizika, 50:3 (2009), 82–96 | MR