Global solutions of semilinear and quasilinear dispersive equations

半线性和拟线性色散方程的全局解

• 批准号: 1265818
• 负责人: Alexandru Ionescu
• 金额: $ 39.7万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1265818&HistoricalAwards=false
• 关键词: Global; solutions; semilinear; quasilinear; dispersive

The PI will study questions related to global existence and long-term dynamics of smooth solutions of certain evolution equations. More precisely, the PI will consider several quasilinear models, such as the Euler-Maxwell system, the Euler-Poisson system, and the irrotational water wave problem in dimensions 2 and 3. The main problems to be considered have to do with the global stability of certain equilibrium solutions of these equations. The PI will also continue his work on the global existence of Schrodinger maps and other spin field systems, in the case of large data.The equations considered in the project describe physical phenomena, such as plasma evolutions, ferromagnetic models, and fluid dynamics, and their relevance is often verified numerically. The PI proposes to study the solutions of these equations rigorously, and recover quantitative and qualitative information about their behavior as mathematical theorems. An important aspect of this proposal is to support the training of graduate students and to foster collaborations with researchers in related fields, such as Physics and Engineering.

PI将研究与全局存在和某些演化方程的平滑解的长期动力学相关的问题。更准确地说，PI将考虑几种拟线性模型，例如Euler-Maxwell系统、Euler-Poisson系统以及2维和3维的无旋水波问题。要考虑的主要问题与全局稳定性有关这些方程的某些平衡解。 PI 还将继续研究大数据情况下薛定谔图和其他自旋场系统的全局存在性。该项目中考虑的方程描述了物理现象，例如等离子体演化、铁磁模型和流体动力学，以及它们的相关性通常通过数字来验证。 PI 建议严格研究这些方程的解，并将有关其行为的定量和定性信息恢复为数学定理。该提案的一个重要方面是支持研究生的培训并促进与物理和工程等相关领域的研究人员的合作。