The Fourth Oklahoma Partial Differential Equations (PDE) Workshop; Oklahoma State University; October 26-27, 2013

该NSF奖支持第四届俄克拉荷马州偏微分方程（PDEs）研讨会，该研讨会将于2013年10月26-27日在俄克拉荷马州立大学（OSU）举行。本次研讨会将介绍几种偏微分方程模拟流体和地球物理流体。其中包括曲面拟地转（SQG）方程、Boussinesq方程和具有特殊空间对称性的三维欧拉方程。在过去的几年里，这些偏微分方程有了非常令人兴奋的新发展，并且在涉及这些偏微分方程的许多基本问题上取得了重大进展，例如全球（时间）正则性问题。本次研讨会受到这些最新进展的启发，努力实现四个主要目标：1)广泛传播重点研究领域的最新进展；2)为当地（俄克拉何马州和邻近州）PDE研究人员提供与领先专家直接交流并接触前沿研究的机会；3)为研究生、新博士、女性和少数族裔提供一个展示研究成果的便利平台；4)促进互动和跨学科合作。偏微分方程是理解从小规模血液流动到大规模地球物理流动等许多流体现象的基本工具。本次研讨会的偏微分方程在许多实际应用中发挥了重要作用，例如研究锋生，冷热空气之间尖锐锋的形成。本次研讨会旨在将重点研究领域的最新研究成果及时介绍给广大受众，并促进数学家和气象学家之间的互动和跨学科合作，包括俄克拉何马州诺曼国家气象中心的气象学家。希望这次研讨会将有助于加速将目前的前沿研究纳入龙卷风等复杂天气现象的建模和模拟中。

This NSF award supports the Fourth Oklahoma Workshop on Partial Differential Equations (PDEs), which will take place at Oklahoma State University (OSU), October 26-27, 2013. This workshop will feature several PDEs modeling fluids and geophysical fluids. Among them are the surface quasi-geostrophic (SQG) equation, the Boussinesq equations and the 3D Euler equations with special spatial symmetries. There are very exciting new developments on these PDEs in the last few years and significant progress has been made on many fundamental issues concerning these PDEs such as the global (in time) regularity problem. This workshop, inspired by these recent advances, strives to fulfill four major objectives: 1) to broadly disseminate the most recent advances in the focused research field; 2) to give local (Oklahoma and neighboring states) PDE researchers an opportunity to communicate directly with the leading experts and to expose themselves to the forefront research; 3) to provide a convenient platform for our graduate students, recent Ph.D.'s, women and minorities to present their research results; and 4) to stimulate interactions and interdisciplinary collaborations.PDEs are fundamental tools in understanding many fluid phenomena ranging from small scale blood flows to large-scale geophysical flows. The PDEs featured by this workshop have played important roles in many practical applications such as in the study of frontogenesis, the formation of sharp fronts between hot and cold air. This workshop aims to bring the state-of-the-art research in the focused research field to a broad audience in a timely fashion and to promote interactions and interdisciplinary collaborations between mathematicians and meteorologists including those in the National Weather Center in Norman, Oklahoma. It is hoped that this workshop will help accelerate the incorporation of the present cutting-edge research into the modeling and simulation of sophisticated weather phenomena such as tornadoes.