U.S.-U.K. Doctoral Dissertation Enhancement Project: The Many Aspects of Fluids

美国-英国博士论文强化项目：流体的多个方面

• 批准号: 0630623
• 负责人: Maria Schonbek
• 金额: $ 1.01万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0630623&HistoricalAwards=false
• 关键词: U.S.; U.K.; Doctoral; Dissertation; Enhancement

OISE 06-30623Schonbek, MariaThis is a project that supports doctoral dissertation enhancement research at Oxford University in the U.K. The U.S. principal investigator and advisor is Maria Schonbek from the University of California, Santa Cruz. Her student is Clayton Bjorland and her U.K. collaborator is Endre Suli. In this project Clayton Bjorland will consider questions related to the existence and asymptotic behavior of a system of nonlinear differential equations: the Viscous Camassa-Holm equations (VCHE), which are also known as Navier-Stokes-alpha equations (NS-alpha). These equations arose from work on shallow water equations. They were also derived as a "filtered" Navier-Stokes equation, which obeys a modified Kelvin circulation theorem along filtered velocities. The Navier-Stokes-alpha equations are closely related the famous Navier-Stokes equations, but the filter allows bounds that are currently unobtainable for the Navier-Stokes equations, and thus makes the NS-alpha equations in some sense better suited for computational turbulence. The hope is that these equations might give good approximations to the Navier-Stokes equations, which are the main model for fluid equations.One of the millennium problems, important classic questions that have resisted solution over the years, from the Clay Institute is in regards to regularity for solutions of the Navier-Stokes equations. The Navier-Stokes equations describe the movement of liquids and gases. Although they were found in the 19th century, they still are not well understood. The problem is to make progress toward a mathematical theory that will give us insight into these equations.

OISE 06- 30623 Schonbek，Maria这是一个支持英国牛津大学博士论文增强研究的项目。 美国首席研究员和顾问是来自加州大学圣克鲁斯的Maria Schonbek。 她的学生是克莱顿比约兰和她的英国。合作者是Endre Suli。在这个项目中，克莱顿Bjorland将考虑与非线性微分方程系统的存在性和渐近行为有关的问题：粘性Camassa-Holm方程（VCHE），也被称为Navier-Stokes-alpha方程（NS-alpha）。这些方程源于浅水方程的工作。它们也被推导为一个“过滤”的纳维-斯托克斯方程，该方程遵循沿着过滤速度的修正的开尔文环流定理。Navier-Stokes-alpha方程与著名的Navier-Stokes方程密切相关，但滤波器允许目前Navier-Stokes方程无法获得的边界，从而使NS-alpha方程在某种意义上更适合计算湍流。我们希望这些方程可以很好地近似Navier-Stokes方程，这是流体方程的主要模型。其中一个千年的问题，重要的经典问题，多年来一直抵制解决方案，从克莱研究所是关于Navier-Stokes方程的解的规律性。Navier-Stokes方程描述了液体和气体的运动。 虽然它们在世纪被发现，但人们对它们的了解仍然不多。 问题是要在数学理论上取得进展，使我们能够深入了解这些方程。