High frequency scattering with applications to fluids

高频散射在流体中的应用

• 批准号: 2576520
• 金额: --
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2576520
• 关键词: frequency; scattering; applications; fluids

The proposed project is part of the primary supervisor's broader research program on spectral and scattering theory. This project focuses on the study of high frequency solutions to wave-type equations. The student's work will focus on the study of scattered waves in the presence of trapping. It has been known since the work of Burq that estimates for such waves must suffer losses relative to non-trapping situations. However, the precise energies at which these losses occur are not fully understood. This project will aim to improve our understanding of this phenomena. While undertaking the project, the student will be trained to use several important theories in mathematics. The student will acquire a strong foundation in mathematical scattering theory as well as in microlocal analysis and functional analysis. These tools have recently found applications in an enormous variety of problems including the study of dynamical systems, internal forced waves in fluids, dynamics of free boundary problems, and general relativity to name a few. The precise understanding of the linearised dynamics is of particular importance in the context of nonlinear PDE. In the course of the project, the student will be trained to look for and implement these tools, particularly in the context of mathematical fluid dynamics; an area of expertise of the secondary supervisor.Research Area: Mathematical analysis

拟议的项目是主要导师关于光谱和散射理论的更广泛研究计划的一部分。该项目重点研究波动型方程的高频解。学生的工作将集中于研究存在俘获的散射波。自从 Burq 的工作以来我们就知道，相对于非陷阱情况，对此类波的估计必然会遭受损失。然而，发生这些损失的确切能量尚不完全清楚。该项目旨在提高我们对这一现象的理解。在开展该项目时，学生将接受培训以使用几种重要的数学理论。学生将获得数学散射理论以及微局域分析和泛函分析的坚实基础。这些工具最近在各种各样的问题中得到了应用，包括动力系统的研究、流体中的内受迫波、自由边界问题的动力学和广义相对论等等。在非线性偏微分方程的背景下，对线性动力学的精确理解尤为重要。在项目过程中，学生将接受培训寻找和实施这些工具，特别是在数学流体动力学的背景下；二级导师的专业领域。研究领域：数学分析