221 research outputs found
The Einstein-Vlasov system/Kinetic theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein-Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on nonrelativistic and special relativistic physics, {\it i.e.} to model
the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems.
In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
({\it i.e.} fluid models). This paper gives introductions to kinetic theory in
non-curved spacetimes and then the Einstein-Vlasov system is introduced. We
believe that a good understanding of kinetic theory in non-curved spacetimes is
fundamental to good comprehension of kinetic theory in general relativity.Comment: 40 pages, updated version, to appear in Living Reviews in Relativit
The Einstein-Vlasov sytem/Kinetic theory
The main purpose of this article is to guide the reader to theorems on global
properties of solutions to the Einstein-Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades where the main focus has
been on nonrelativistic- and special relativistic physics, e.g. to model the
dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In
1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
(e.g. fluid models). The first part of this paper gives an introduction to
kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is
introduced. We believe that a good understanding of kinetic theory in
non-curved spacetimes is fundamental in order to get a good comprehension of
kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity
(http://www.livingreviews.org
Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions
A finite Larmor radius approximation is derived from the classical Vlasov
equation, in the limit of large (and uniform) external magnetic field. We also
provide an heuristic derivation of the electroneutrality equation in the finite
Larmor radius setting. Existence and uniqueness of a solution is proven in the
stationary frame for solutions depending only on the direction parallel to the
magnetic field and factorizing in the velocity variables
The Cauchy problem for the 3-D Vlasov-Poisson system with point charges
In this paper we establish global existence and uniqueness of the solution to
the three-dimensional Vlasov-Poisson system in presence of point charges in
case of repulsive interaction. The present analysis extends an analogeous
two-dimensional result by Caprino and Marchioro [On the plasma-charge model, to
appear in Kinetic and Related Models (2010)].Comment: 28 page
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