Mathematical Sciences: Some Mathematical Problems in Meteorology, Oceanography and Climatology

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9623071 Wang The investigators studies the partial differential equations arising in meteorology, oceanography and climatology. The work is the mathematical analysis part of an ongoing project, jointly with J. L. Lions (College de France) and R. Temam (Indiana University); that project involves a combination of modeling, mathematical theory, and scientific computing. Among the partial differential equations are the core equations in climatology such as the primitive equations of the atmosphere-only, the ocean-only, and the coupled atmosphere/ocean systems. Part of the mathematical theory has been attained in previous work about these core equations of the atmosphere, ocean and coupled atmosphere-ocean. A large amount of work such as the existence and properties of strong solutions and long time behavior remains to be done, however. Also, the mathematical analysis of sea ice equations and some free surface models is also addressed. Another part of the proposed work is to justify from the mathematical viewpoint the geostrophic asymptotics and the associated quasi-geostrophic equations (well-posedness and long time dynamics). The phenomena of the atmosphere and ocean are extremely rich in organization and complexity. The study of these complicated phenomena and the relevant scientific issues are very challenging and necessitate a joint effort of scientists in many fields. The proposed work takes up this study from the mathematical point of view. As is now well-known and as pointed out by John von Neumann in the fifties, understanding and prediction of the weather and climate involve a great deal of mathematical analysis and a great deal of calculation. This project aims at a better understanding of the mechanisms of the turbulent behavior of the air and seawater, as well as tools for better prediction of the weather and possible global change.