Functional and harmonic analysis of function spaces: synthesis, development and applications

函数空间的泛函和调和分析：综合、开发和应用

• 批准号: DP0881037
• 负责人: Dr Sergey Ajiev
• 金额: $ 16.04万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2008
• 资助国家: 澳大利亚
• 起止时间: 2008-01-01 至 2011-03-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0881037
• 关键词: Functional; harmonic; analysis; function; spaces

Recent advances in mathematics are on the borderlines of its branches. This interdisciplinary project develops and binds the research areas attracting growing interest of prominent mathematicians during the last 30 years because of not only its theoretical value, but also its ties with the key equations describing a multitude of physical phenomena and the theoretical foundation of numerical methods. The Euler, Helmholtz, Lamb, Navier-Stokes and acoustic equations, studied in terms of function spaces, govern incompressible viscous fluid flows and wave propagations. Contributing to both pure mathematics and, particularly, Short-Term Tsunami Prediction, the project will enhance Australia's research reputation.

数学的最新进展是在其分支的边缘。 这个跨学科的项目开发和绑定的研究领域吸引了杰出的数学家在过去的30年里，因为不仅其理论价值，而且它与描述众多物理现象的关键方程和数值方法的理论基础的关系日益增长的兴趣。在函数空间中研究的欧拉、亥姆霍兹、兰姆、纳维尔-斯托克斯和声学方程支配着不可压缩粘性流体流动和波的传播。该项目对纯数学，特别是短期海啸预测都有贡献，将提高澳大利亚的研究声誉。