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.

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 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.

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.

Any large solution of a non-linear heat conduction equation becomes monotonic in time

1991 ◽  
Vol 118 (1-2) ◽  
pp. 13-20 ◽  
Author(s):  
Victor A. Galaktionov ◽  
Sergey A. Posashkov
Keyword(s):  
Parabolic Equation ◽  
Initial Function ◽  
Heat Conduction Equation ◽  
Stationary Solutions ◽  
Classical Solutions ◽  
Smooth Functions ◽  
Large Solution ◽  
Additional Hypothesis ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

SynopsisIn this paper we prove a certain monotonicity in time of non-negative classical solutions of the Cauchy problem for the quasilinear uniformly parabolic equation u1 = (ϕ(u))xx + Q(u) in wT = (0, T] × R1 with bounded sufficiently smooth initial function u(0, x) = uo(x)≧0 in Rl. We assume that ϕ(u) and Q(u) are smooth functions in [0, +∞) and ϕ′(u) >0, Q(u) > 0 for u > 0. Under some additional hypothesis on the growth of Q(u)ϕ′(u) at infinity, it is proved that if u(to, xo) becomes sufficiently large at some point (to, xo) ∈ wT, then ut(t, x0) ≧0 for all t ∈ [t0, T]. The proof is based on the method of intersection comparison of the solution with the set of the stationary solutions of the same equation. Some generalisations of this property for a quasilinear degenerate parabolic equation are discussed.

THE BLACK HOLE ENTROPY BOUND AND THE MAXIMUM TEMPERATURE FOR MESON FORMATION IN THE NUCLEAR FIREBALL

1991 ◽  
Vol 06 (33) ◽  
pp. 3039-3045 ◽  
Author(s):  
JISHNU DEY ◽  
MIRA DEY ◽  
MARCELO SCHIFFER ◽  
LAURO TOMIO
Keyword(s):  
Black Hole ◽  
Simple Model ◽  
Black Hole Entropy ◽  
Heavy Ion ◽  
Black Hole Thermodynamics ◽  
Maximum Temperature ◽  
Ion Collisions ◽  
Pion Interferometry ◽  
Entropy Bound ◽  
Confined System

The entropy bound from black hole thermodynamics can be invoked to set limits for temperatures at which hadrons can survive as a confined system. We find that this implies that the pion can be formed in heavy ion collisions, much later than heavier mesons, for example the ρ-meson, when the fireball is cooler. The temperature found in a simple model agree qualitatively with experiment. We also suggest that this may be the reason why in pion interferometry experiments the space-time volume of the pion source seems large.

Global Existence for the Two-Dimensional Euler Equations in a Critical Besov Space

2011 ◽  
Vol 271-273 ◽  
pp. 791-796
Author(s):  
Kun Qu ◽  
Yue Zhang
Keyword(s):  
Global Existence ◽  
Transport Equation ◽  
Besov Space ◽  
Euler Equations ◽  
Existence Result ◽  
Two Dimensional ◽  
Critical Besov Space ◽  
Global Existence Result

In this paper we prove the global existence for the two-dimensional Euler equations in the critical Besov space. Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the global existence result.

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.

On a critical nonlinear problem involving the fractional Laplacian

2021 ◽  
pp. 2150066
Author(s):  
Azeb Alghanemi ◽  
Hichem Chtioui
Keyword(s):  
Global Existence ◽  
Bounded Domain ◽  
Nonlinear Problem ◽  
Fractional Laplacian ◽  
Existence Result ◽  
Counting Formula ◽  
Global Existence Result

Fractional Yamabe-type equations of the form [Formula: see text] in [Formula: see text] on [Formula: see text], where [Formula: see text] is a bounded domain of [Formula: see text], [Formula: see text] is a given function on [Formula: see text] and [Formula: see text], is the fractional Laplacian are considered. Bahri’s estimates in the fractional setting will be proved and used to establish a global existence result through an index-counting formula.

Sign in / Sign up

Export Citation Format

Share Document