Qualitative studies of the Navier-Stokes and related systems

纳维-斯托克斯及相关系统的定性研究

• 批准号: 1311943
• 负责人: Igor Kukavica
• 金额: $ 25.62万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311943&HistoricalAwards=false
• 关键词: Qualitative; studies; Navier; Stokes; related

The project addresses qualitative properties of solutions of the Navier-Stokes and related equations arising in fluid dynamics, including the Euler and Primitive equations. We will investigate the properties of small scales in a turbulent flow by estimating the complexity of solutions and study the relationship with the problems regarding observables and degrees of freedom in a fluid. A considerable effort will be dedicated to a fluid-structure models (local and global existence, regularity) and other complex PDE systems involving a fluid boundary. We will also study the properties solutions of the viscous and inviscid primitive equation of the ocean and the atmosphere. We will especially be interested in local and global existence of solutions and their asymptotic behavior.The mathematical study of fluids is of fundamental importance in meteorology, science, and engineering. The project seeks better understanding of the fluid motion especially on small scales which are of interest in turbulence. The special emphasis is going to be placed on the primitive equations which constitute the basic model for weather prediction and on the fluid-structure systems modeling interaction of a fluid with an elastic body.

该项目解决了流体动力学中出现的Navier-Stokes方程和相关方程的解的定性性质，包括欧拉方程和原始方程。我们将通过估计解的复杂性来研究湍流中小尺度的性质，并研究与流体中可观测值和自由度问题的关系。相当多的工作将致力于流体结构模型（局部和全局存在性、规律性）和其他涉及流体边界的复杂偏微分方程系统。我们还将研究海洋和大气的粘性和非粘性原始方程的性质解。我们将特别关注解的局部和全局存在性及其渐近性。流体的数学研究在气象学、科学和工程中具有根本的重要性。该项目寻求更好地理解流体运动，特别是在湍流感兴趣的小尺度上。特别强调的是构成天气预报基本模型的原始方程，以及模拟流体与弹性体相互作用的流固系统。