NDLI: Equation of a Barotropic Fluid on a Rotating Spherical Surface and its Inertial Manifold

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Equation of a Barotropic Fluid on a Rotating Spherical Surface and its Inertial Manifold

Content Provider	Springer Nature Link
Author	Horák, J.
Copyright Year	2000
Abstract	The inertial manifold is a positive invariant set which exponentially attracts all the trajectories of a dissipative dynamic system. It was introduced for the purpose of studying the asymptotic behaviour of such systems. The initial infinitely dimensional dynamic system, generated by a partial differential evolution equation, can be projected on to it, in order to obtain the final system of ordinary differential equations (inertial equations). These equations then simulate the initial object. Although the inertial manifold is an object relatively simpler than the attractor (a very complicated set of non-integer dimension may be an attractor) it is more difficult to prove its existence than that of the attractor. The equation of a barotropic fluid on a rotating spherical surface is one of the examples of dissipative dynamic systems with an inertial manifold. This kindles the hope that also the equations of the dynamics of the real atmosphere will have an inertial manifold. The reduction of the sample system to this Lipschitz manifold of finite dimension thus justifies us in analysing the behaviour of the atmosphere on non-linear models of finite dimensions and few parameters, in a finite system of ordinary differential equations.
Starting Page	26
Ending Page	37
Page Count	12
File Format	PDF
ISSN	00393169
Journal	Studia Geophysica et Geodaetica
Volume Number	44
Issue Number	1
e-ISSN	15731626
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2000-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Structural Geology Geophysics/Geodesy Meteorology/Climatology
Content Type	Text
Resource Type	Article
Subject	Geochemistry and Petrology Geophysics

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