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New formulations of the primitive equations of atmosphere and applications. (English) Zbl 0746.76019
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.

76B60Atmospheric waves
86A10Meteorology and atmospheric physics
35Q35PDEs in connection with fluid mechanics
37C70Attractors and repellers, topological structure
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