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.

scholarly journals Stability of disk-like galaxies – Part I: Stability via reduction

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Roman Fiřt ◽  
Gerhard Rein
Keyword(s):  
Stability Problem ◽  
Variational Approach ◽  
Steady States ◽  
Poisson System ◽  
Reduction Procedure ◽  
Analogous Question ◽  
Existence And Stability ◽  
The Stability

We prove the existence and stability of flat steady states of the Vlasov–Poisson system, which in astrophysics are used as models of disk-like galaxies. We follow the variational approach developed by GUO and REIN [5, 6, 7] for this type of problems and extend previous results of REIN [11]. In particular, we employ a reduction procedure which relates the stability problem for the Vlasov–Poisson system to the analogous question for the Euler–Poisson system.

Stability of disk-like galaxies – Part II: The Kuzmin disk

Analysis ◽  
2007 ◽  
Vol 27 (4) ◽  
Author(s):  
Roman Fiřt
Keyword(s):  
Steady State ◽  
Nonlinear Stability ◽  
Variational Approach ◽  
Poisson System ◽  
Finite Mass

SummaryWe prove the existence and nonlinear stability of the Kuzmin disk, a polytropic steady state of the Vlasov–Poisson system widely used in astrophysics, which has infinite support, but finite mass. As in Part I we use the variational approach by REIN and GUO.

SOME ASYMPTOTICS FOR A REACTIVE NAVIER–STOKES–POISSON SYSTEM

1999 ◽  
Vol 09 (07) ◽  
pp. 1039-1076 ◽  
Author(s):  
B. DUCOMET
Keyword(s):  
Global Existence ◽  
Global Solution ◽  
Spherical Model ◽  
Navier Stokes ◽  
Positive Energy ◽  
Stability Of Solutions ◽  
Poisson System ◽  
Rigid Core ◽  
Existence And Stability

We prove global existence and stability of solutions for a spherical model of reactive compressible self-gravitating fluid when a rigid core is present. In the absence of core, we show that no global solution of positive energy can exist.

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
Sign in / Sign up

Export Citation Format

Share Document