Partial differential equation: Schrodinger operator and long-time dynamics

偏微分方程：薛定谔算子和长期动力学

• 批准号: FT230100588
• 负责人: A/Prof Zihua Guo
• 金额: $ 72.6万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-06-30 至 2028-06-29
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT230100588
• 关键词: Partial; differential; equation; Schrodinger; operator; Partial; differential; equation; Schrodinger; operator

This project aims to develop new analysis methods associated to the Schrodinger operator, and to solve several challenging problems regarding dispersive partial differential equations (PDE). Long-time dynamics of PDE solutions are a key goal in both pure and applied mathematics, and have been extensively studied by leading mathematicians and mathematical physicists. However, it is unknown how to investigate large solutions when the order of the PDE's nonlinearity is low. This project expects to develop new methods to attack such problems. The results of the project will be of great importance in mathematics and physics, as many fundamental physical models in areas such as optics, fluid mechanics and quantum mechanics fit the paradigm.

该项目旨在开发与Schrodinger操作员相关的新分析方法，并解决有关分散部分微分方程（PDE）的几个具有挑战性的问题。 PDE解决方案的长期动力学是纯数学和应用数学的关键目标，并且已由领先的数学家和数学物理学家进行了广泛的研究。但是，当PDE的非线性阶段较低时，如何研究大型解决方案是未知的。该项目希望开发新的方法来攻击此类问题。该项目的结果将在数学和物理学中非常重要，因为在光学，流体力学和量子力学等领域的许多基本物理模型都适合范式。