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The periodic quasigeostrophic equations: existence and uniqueness of strong solutions

Bennett, A.F. and Kloeden, P.E. (1982) The periodic quasigeostrophic equations: existence and uniqueness of strong solutions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 91 (3-4). pp. 185-203.

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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.

Item Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: University of California Press
Copyright: © Royal Society of Edinburgh 1982
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