Long Term Regularity of Solutions of Fluid Models

流体模型解的长期规律性

• 批准号: 1600028
• 负责人: Alexandru Ionescu
• 金额: $ 31.82万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1600028&HistoricalAwards=false
• 关键词: Long; Term; Regularity; Solutions; Fluid

This research project studies a class of partial differential equations that describe physical phenomena including water waves, plasmas, and gravitation. The complicated nature of the solutions to such equations often precludes complete mathematical analysis, and applications rely on numerical approximations. This project studies the solutions of these equations rigorously and recovers quantitative and qualitative information about their behavior as mathematical theorems. The project involves graduate students and postdoctoral associates in the research and fosters collaborations with researchers in related fields, including physics and engineering. This project studies the solutions of several quasilinear dispersive partial differential equations, including water-wave models in two and three spatial dimensions, the more general case of two-fluid interfaces, and the Einstein-Klein-Gordon equations of general relativity. The main problems under study concern the global stability of the equilibrium solutions of these equations and the construction of solutions that become singular in finite time. The project aims to contribute new methods and tools to this dynamic field.

该研究项目研究一类描述水波、等离子体和引力等物理现象的偏微分方程。 此类方程解的复杂性通常妨碍完整的数学分析，并且应用依赖于数值近似。 该项目严格研究这些方程的解，并将有关其行为的定量和定性信息恢复为数学定理。该项目让研究生和博士后参与研究，并促进与物理和工程学等相关领域研究人员的合作。该项目研究几个拟线性色散偏微分方程的解，包括两个和三个空间维度的水波模型、二流体界面的更一般情况以及广义相对论的爱因斯坦-克莱因-戈登方程。研究的主要问题涉及这些方程平衡解的全局稳定性以及在有限时间内变得奇异的解的构造。该项目旨在为这个充满活力的领域贡献新的方法和工具。