Mathematical problems in collisionless kinetic theory.

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，如牛顿引力或静电学的泊松方程、电磁的麦克斯韦方程或广义相对论的爱因斯坦方程。后两者是双曲型方程。目前，在某些显式定常解的邻域内对这些方程的解的研究取得了很大进展。该项目的目的是采用近年来发展起来的非线性偏微分方程解的技巧，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。该项目属于EPSRC的数学科学战略主题，研究领域包括数学分析、数学物理和非线性系统。

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.