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与场方程耦合的弗拉索夫方程，例如牛顿引力或静电学的泊松方程、电磁学的麦克斯韦方程或广义相对论的爱因斯坦方程。后两个是双曲方程。目前正在取得很大的进展，这些方程的解决方案，在某些显式的定态解的邻域的研究。该项目的目的是调整近年来开发的非线性偏微分方程的技术，以解决与这些方程解的渐近行为和整体存在性质有关的问题。该项目福尔斯属于EPSRC数学科学的战略主题，以及数学分析，数学物理和非线性系统的研究领域。