Mathematical problems in collisionless kinetic theory.

无碰撞动力学理论中的数学问题。

• 批准号: 2620319
• 金额: --
• 依托单位: Imperial 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: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2620319
• 关键词: Mathematical; problems; collisionless; kinetic; theory.

The project involves addressing certain problems in collisionless kinetic theory. Collisionless kinetic theory concerns the Vlasov equation coupled to field equations such as the Poisson equation of Newtonian gravity or electrostatics, the Maxwell equations of electromagnetism, or the Einstein equations of general relativity. The latter two are hyperbolic equations. Great progress is currently being made on the study of solutions of these equations in neighbourhoods of certain explicit stationary solutions. The aim of the project is to adapt techniques in nonlinear partial differential equations, developed over recent years, to address problems related to the asymptotic behaviour and global existence properties of solutions of these equations. The project falls under the EPSRC strategic theme of mathematical sciences, and the research areas of mathematical analysis, mathematical physics, and nonlinear systems.

该项目涉及解决无碰撞动力学理论中的某些问题。无碰撞动力学理论涉及弗拉索夫方程与田间方程（例如牛顿重力或静电的泊松方程，电磁主义的麦克斯韦方程）或一般相对性的爱因斯坦方程。后两个是双曲线方程。目前，在某些明确的固定解决方案的社区中，目前正在研究这些方程的解决方案的解决方案。该项目的目的是适应近年来开发的非线性偏微分方程中的技术，以解决与这些方程式解决方案的渐近行为和全球存在性质有关的问题。该项目属于数学科学的EPSRC战略主题，以及数学分析，数学物理学和非线性系统的研究领域。