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The periodic quasigeostrophic equations: existence and uniqueness of strong solutions

Published online by Cambridge University Press:  14 November 2011

A. F. Bennett  and
P. E. Kloeden
A. F. Bennett
Affiliation:
Department of Mathematics, Monash University, Clayton 3168, Victoria, Australia
P. E. Kloeden
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch 6153, Western Australia
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Synopsis

The periodic quasigeostrophic equations are a coupled system of a second order elliptic equation for a streamfunction and first order hyperbolic equations for the relative potential vorticity and surface potential temperatures, on a three-dimensional domain which is periodic in both horizontal spatial co-ordinates. Such equations are used in both numerical and theoretical studies in meteorology and oceanography. In this paper Schauder estimates and a Schauder fixed point theorem are used to prove the existence and uniqueness of strong, that is classical, solutions of the periodic quasigeostrophic equations for a finite interval of time, which is inversely proportional to the sum of the norms of the initial vorticity and surface temperatures.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 3-4 , 1982 , pp. 185 - 203
Copyright
Copyright © Royal Society of Edinburgh 1982

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