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

这一NSF奖项支持将于2013年10月26-27日在俄克拉荷马州立大学(OSU)举行的第四届俄克拉荷马州偏微分方程(PDE)研讨会。该研讨会将以几个PDE模拟流体和地球物理流体为特色。其中包括地表准地转(SQG)方程、Boussinesq方程和具有特殊空间对称性的三维Euler方程。在过去的几年里，关于这些偏微分方程有了非常令人振奋的新进展，并且在与这些偏微分方程有关的许多基本问题上取得了重大进展，例如全球(及时)规律性问题。这个研讨会受到这些最新进展的启发，致力于实现四个主要目标：1)广泛传播重点研究领域的最新进展；2)让当地(俄克拉荷马州和邻近州)的PDE研究人员有机会与领先的专家直接交流，并接触到前沿研究；3)为我们的研究生、新近的博士S、女性和少数族裔提供一个方便的平台，介绍他们的研究成果；以及4)促进互动和跨学科合作。该讲习班所展示的偏微分方程在许多实际应用中发挥了重要作用，例如在研究锋生、冷热空气之间尖锐锋面的形成等方面。这次研讨会的目的是将重点研究领域的最新研究及时带给广大受众，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市国家气象中心的那些人。希望这次讲习班将有助于加速将目前的尖端研究纳入龙卷风等复杂天气现象的建模和模拟。

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.