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Zbl 0746.76019
Lions, Jacques Louis; Temam, Roger; Wang, Shouhong
New formulations of the primitive equations of atmosphere and applications. (English)
[J] Nonlinearity 5, No.2, 237-288 (1992). ISSN 0951-7715; ISSN 1361-6544/e

Summary: The primitive equations are the fundamental equations of atomospheric dynamics. With the purpose of understanding the mechanism of long-term weather prediction and climate changes, we study in this paper as a first step towards the long-range project what is widely considered as the basic equations of atmospheric dynamics in meteorology, namely the primitive equations of atmosphere. The mathematical formulation and attractors of the primitive equations, with or without vertical viscosity, are studied. First of all, by integrating the diagnostic equations we present a mathematical setting, and obtain the existence and time analyticity of solutions to the equations. We then establish some physically relevant estimates for the Hausdorff and fractal dimensions of the attractors of the problems.

MSC 2000:: *76B60 Atmospheric waves
86A10 Meteorology
35Q35 Other equations arising in fluid mechanics
37C70 Attractors and repellers, topological structure

Keywords: long-term weather prediction; climate changes; attractors; vertical viscosity; existence; time analyticity of solutions; Hausdorff and fractal dimensions

Cited in: Zbl 1018.01014 Zbl 1030.86004 Zbl 0837.35030 Zbl 0794.58026

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