Lions, Jacques Louis; Temam, Roger; Wang, Shouhong New formulations of the primitive equations of atmosphere and applications. (English) Zbl 0746.76019 Nonlinearity 5, No. 2, 237-288 (1992). 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. Cited in 5 ReviewsCited in 213 Documents MSC: 76B60 Atmospheric waves (MSC2010) 86A10 Meteorology and atmospheric physics 35Q35 PDEs in connection with fluid mechanics 37C70 Attractors and repellers of smooth dynamical systems and their topological structure Keywords:long-term weather prediction; climate changes; attractors; vertical viscosity; existence; time analyticity of solutions; Hausdorff and fractal dimensions PDFBibTeX XMLCite \textit{J. L. Lions} et al., Nonlinearity 5, No. 2, 237--288 (1992; Zbl 0746.76019) Full Text: DOI