NEW FORMULATIONS OF THE PRIMITIVE EQUATIONS OF ATMOSPHERE AND APPLICATIONS

The primitive equations are the fundamental equations of atmospheric 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 this 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.