Stationary Solutions of the Flat Vlasov–Poisson System

2018 ◽  
Vol 231 (1) ◽  
pp. 189-232 ◽  
Author(s):  
Jürgen Batt ◽  
Enno Jörn ◽  
Yi Li
Keyword(s):  
Stationary Solutions ◽  
Poisson System

Existence and stability of static shells for the Vlasov–Poisson system

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Achim Schulze
Keyword(s):  
Spherical Symmetry ◽  
Variational Approach ◽  
Stationary Solutions ◽  
Poisson System ◽  
Existence And Stability

We prove the existence and stability of stationary solutions to the Vlasov–Poisson System with spherical symmetry, which describe static shells, i.e., the support of their densities is bounded away from the origin. We use a variational approach which was established by Y. Guo and G. Rein.

scholarly journals Existence and stability of static shells for the Vlasov–Poisson system with a fixed central point mass

2009 ◽  
Vol 146 (2) ◽  
pp. 489-511
Author(s):  
ACHIM SCHULZE
Keyword(s):  
Black Hole ◽  
Simple Model ◽  
Variational Approach ◽  
Existence Result ◽  
Stationary Solutions ◽  
Point Mass ◽  
Classical Solutions ◽  
Poisson System ◽  
Existence And Stability ◽  
Global Existence Result

AbstractWe consider the Vlasov–Poisson system with spherical symmetry and an exterior potential which is induced by a point mass in the center. This system can be used as a simple model for a newtonian galaxy surrounding a black hole. For this system, we establish a global existence result for classical solutions with shell-like initial data, i.e. the support of the density is bounded away from the point mass singularity. We also prove existence and stability of stationary solutions which describe static shells, where we use a variational approach which was established by Y. Guo and G. Rein.

Stationary Solutions of the Vlasov–Poisson System with Diffusive Boundary Conditions

2015 ◽  
Vol 25 (2) ◽  
pp. 315-342 ◽  
Author(s):  
Emre Esentürk ◽  
Hyung Ju Hwang ◽  
Walter A. Strauss
Keyword(s):  
Boundary Conditions ◽  
Stationary Solutions ◽  
Poisson System ◽  
Diffusive Boundary

scholarly journals SINGULARITIES OF STATIONARY SOLUTIONS TO THE VLASOV–POISSON SYSTEM IN A POLYGON

2013 ◽  
Vol 23 (06) ◽  
pp. 1029-1066 ◽  
Author(s):  
FAHD KARAMI ◽  
SIMON LABRUNIE ◽  
BRUNO PINÇON
Keyword(s):  
Distribution Function ◽  
Numerical Experiments ◽  
Total Mass ◽  
Existence Result ◽  
Equilibrium Distribution ◽  
Stationary Solutions ◽  
Equilibrium Distribution Function ◽  
Poisson System ◽  
Singular Behavior ◽  
Plane Polygon

We present an existence result for the stationary Vlasov–Poisson system in a bounded domain of ℝN, with more general hypotheses than considered so far in the literature. In particular, we prove the equivalence of the kinetic approach (which consists in looking for the equilibrium distribution function) and the potential approach (where the unknown is the electrostatic potential at equilibrium). We study the dependence of the solution on parameters such as the total mass of the distribution, or those entering in the boundary conditions of the potential. Focusing on the case of a plane polygon, we study the singular behavior of the solution near the re-entrant corners, and examine the dependence of the singularity coefficients on the parameters of the problem. Numerical experiments illustrate and confirm the analysis.

scholarly journals Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions

1995 ◽  
Vol 130 (2) ◽  
pp. 163-182 ◽  
Author(s):  
J�rgen Batt ◽  
Philip J. Morrison ◽  
Gerhard Rein
Keyword(s):  
Linear Stability ◽  
Stationary Solutions ◽  
Three Dimensions ◽  
Poisson System
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