Harmonic analysis and dispersive partial differential equations

本项目旨在发展偏微分方程研究的理论成果和实用技术。调和分析是用来研究这些方程;在其中一个系统的局部行为是用来分析全球的财产，使用技术，如傅立叶变换。该项目将研究该领域的核心问题，揭示分析和几何之间的深层联系，并将其应用于研究非线性方程的解决方案的长期行为。预期成果包括解决量子和流体力学中出现的非线性色散方程的理论结果和实用技术。

This project aims to develop theoretical results and practical techniques in the study of Partial Differential Equations. Harmonic analysis is used to study these equations; in which a system’s local behaviour is used to analyse global properties, using techniques such as the Fourier transform. The project will investigate central problems in the area, revealing deep connections between analysis and geometry, and apply these to study the solutions’ long-term behaviour to non-linear equations. Expected outcomes include theoretical results and practical techniques to solve non-linear dispersive equations, which arise in quantum and fluid mechanics.