Mathematical Sciences: Aspects of Compressible and Incompressible Flows

数学科学：可压缩和不可压缩流的方面

• 批准号: 9020941
• 负责人: Maria Schonbek
• 金额: $ 6万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9020941&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Aspects; Compressible; Incompressible

The principal investigator will study certain qualitative properties of incompressible viscous fluids, compressible fluids and mixtures of fluids by using techniques of modern functional analysis and numerical analysis. In particular, she will study the long-time asymptotic behavior of solutions of the Navier-Stokes equations in two and three space dimensions, the equations of incompressible magnetohydrodynamics in three dimensions, and some integro-differential equations that model compressible flows. She will also investigate the global existence in time of solutions of a set of multiphase equations. Very often one is interested in the behavior of a physical system only after a long time. For example, once a process is started one might expect that a single type of stable behavior is the dominant observable output. Deviations from this stable behavior might be very much unwanted. The principal investigator will devote most of her efforts to study how various real-world fluid systems behave for a very long time by using modern techniques from applied mathematics and numerical analysis.

首席研究员将研究某些定性的 不可压缩粘性流体、可压缩流体的性质 和流体的混合物通过使用现代功能的技术， 分析和数值分析。 特别是，她将研究 Navier-Stokes方程解的长时间渐近性态 二维和三维空间中的方程， 三维不可压缩磁流体力学，以及一些 模拟可压缩流的积分微分方程。 她 还将研究的整体存在的时间的解决方案 一组多相方程 很多时候，人们对一个物理行为感兴趣， 系统只是经过很长一段时间。 例如，一旦一个进程 开始时，人们可能会认为一种单一类型的稳定行为是 占主导地位的可观察输出。 偏离此稳定 行为可能非常不受欢迎。 主要研究者 她将把大部分精力投入到研究现实世界中的各种 流体系统的行为很长一段时间，通过使用现代 应用数学和数值分析的技术。