Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting
نویسندگان
چکیده
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.
منابع مشابه
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
The Vlasov-Poisson system is a classical model in physics used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of classical solutions is limited to dimensions d ≤ 3 under strong assumptions on the initial data, while weak solutions are known to exist under milder conditions. However, in the setting of weak solutions it is unclear...
متن کاملGlobal classical solutions of the Vlasov-Darwin system for small initial data
A global-in-time existence theorem for classical solutions of the Vlasow-Darwin system is given under the assumption of smallness of the initial data. Furthermore it is shown that in case of spherical symmetry the system degenerates to the relativistic Vlasov-Poisson system.
متن کاملL Stability for the Vlasov-poisson-boltzmann System around Vacuum
Based on the global existence theory of the Vlasov-Poisson-Boltzmann system around vacuum in the N -dimensional phase space, in this paper, we prove the uniform L1 stability of classical solutions for small initial data when N ≥ 4. In particular, we show that the stability can be established directly for the soft potentials, while for the hard potentials and hard sphere model it is obtained thr...
متن کاملGlobal Solutions for the One-dimensional Vlasov-maxwell System for Laser-plasma Interaction
We analyse a reduced 1D Vlasov–Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an electrostatic field obtained from Poisson’s equation and a vector potential term satisfying a nonlinear wave equation. Both nonlinearities in the Poisson and wave equ...
متن کاملFlat steady states in stellar dynamics—existence and stability
We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a ma...
متن کامل