Advances in the theory of dispersive equations

色散方程理论的进展

• 批准号: 0602678
• 负责人: Gigliola Staffilani
• 金额: --
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0602678&HistoricalAwards=false
• 关键词: Advances; theory; dispersive; equations

Advances in the Theory of Dispersive Equations Abstract of Proposed ResearchGigliola Staffilani This project is to study the well posedness of dispersive partial differential equations, with particular emphasis on the nonlinear Schroedinger equation. That is, how much regularity must one impose on the initial data to insure existence and uniqueness of the solutions at later times? Also what regularity is preserved and what is the asymptotic behavior of the solutions? Recent advances in the theory of nonlinear dispersive equations have been driven by the introduction of sophisticated methods and new techniques from Fourier and harmonic analysis. This proposal is to further pursue these new directions and to better understand their implications.

色散方程理论的进展拟议研究摘要Gigliola Staffilani 本计画主要研究色散偏微分方程的适定性，特别是非线性薛定谔方程。也就是说，我们必须对初始数据施加多大的正则性，才能确保以后解的存在性和唯一性？还有什么正则性是保持的，解的渐近行为是什么？非线性色散方程理论的最新进展是由傅立叶和谐波分析的复杂方法和新技术的引入所推动的。 本建议旨在进一步探讨这些新方向，并更好地理解其影响。