Global existence of classical solutions to the vlasov-poisson system in a three-dimensional, cosmological setting

Abstract

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.

Small Data Solutions of the Vlasov-Poisson System and the Vector Field Method

“…for some σ > 0, which has enough decay so that it remains integrable in t even when multiplied by the extra t weight of (25). Putting everything together, we have obtain…”

The Vlasov-Poisson System with Radiation Damping

“…Thus we obtain a solution of the Vlasov-Poisson system where the potential W does not satisfy the usual boundary conditions. This is similar to the cosmological solutions of the Vlasov-Poisson system constructed in [23]. They are obtained directly as solutions of a transformed system but are in the end solutions of the Vlasov-Poisson system with unconventional boundary conditions.…”

Уравнения Власова - Пуассона Для Двукомпонентной Плазмы В Однородном Магнитном Поле

“…В четырехмерном случае Э. Хорстом [56] было доказано, что задача Коши для системы урав-нений Власова-Пуассона может не иметь глобального классического решения. Классические решения начальной задачи для уравнений Власова-Пуассона ис-следовались также в работах [3], [18], [44], [45], [57], [74], [75], [97], [98] и др.…”