This article is cited 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.

UDC: 533+517.958

Received: 16.03.2011

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