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The dissipative quasigeostrophic equations

Published online by Cambridge University Press:  26 February 2010

A. F. Bennett
Affiliation:
Mathematics Department, Monash University, Clayton 3168, Australia.
P. E. Kloeden
Affiliation:
Mathematics Department, Monash University, Clayton 3168, Australia.
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Abstract

Existence and uniqueness of classical solutions are established for the dissipative quasigeostrophic equations of geophysical fluid dynamics, using a priori estimates and a Schauder fixed point theorem. The flow is periodic in both horizontal directions and is bounded above and below by rigid flat surfaces. The Reynolds analogy of unit turbulent Prandtl number is assumed. Existence is proved for an arbitrary finite time, if it is further assumed that the surface temperatures vanish. Without this additional assumption existence is guaranteed only for a certain finite time, which is inversely proportional to the norms of the sources and initial conditions.

Type
Research Article
Copyright
Copyright © University College London 1981

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