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

9623071研究人员研究气象学、海洋学和气候学中的偏微分方程。这项工作是与J.L.Lions(法国学院)和R.Temam(印第安纳大学)共同开展的一个正在进行的项目的数学分析部分；该项目涉及建模、数学理论和科学计算的组合。在偏微分方程组中有气候学的核心方程，如纯大气、纯海洋和大气/海洋耦合系统的原始方程。关于大气、海洋和海-气耦合这些核心方程的部分数学理论已经在前人的工作中得到了。然而，仍然有大量的工作要做，例如强解的存在性和性质以及长时间行为。文中还讨论了海冰方程和一些自由面模型的数学分析。另一部分工作是从数学的角度证明地转渐近性和相关的准地转方程(适定性和长时间动力学)。大气和海洋现象具有极强的组织性和复杂性。研究这些复杂的现象和相关的科学问题是非常具有挑战性的，需要许多领域的科学家共同努力。拟议的工作从数学角度对这一研究进行了研究。众所周知，正如约翰·冯·诺伊曼在50年代指出的那样，对天气和气候的理解和预测涉及大量的数学分析和大量的计算。该项目旨在更好地了解空气和海水的湍流行为的机制，以及更好地预测天气和可能的全球变化的工具。

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.