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Kinetic and Related Models (KRM)
 

Unstable galaxy models

Pages: 701 - 714, Volume 6, Issue 4, December 2013      doi:10.3934/krm.2013.6.701

 
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Zhiyu Wang - School of Mathematical Sciences, Peking University, Beijing, 100871, China (email)
Yan Guo - Division of Applied Mathematics, Brown University, Providence, RI 02912, United States (email)
Zhiwu Lin - School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States (email)
Pingwen Zhang - School of Mathematical Sciences, Peking University, Beijing, 100871, China (email)

Abstract: The dynamics of collisionless galaxy can be described by the Vlasov-Poisson system. By the Jean's theorem, all the spherically symmetric steady galaxy models are given by a distribution of $\Phi(E,L)$, where $E$ is the particle energy and $L$ the angular momentum. In a celebrated Doremus-Feix-Baumann Theorem [7], the galaxy model $\Phi(E,L)$ is stable if the distribution $\Phi$ is monotonically decreasing with respect to the particle energy $E.$ On the other hand, the stability of $\Phi(E,L)$ remains largely open otherwise. Based on a recent abstract instability criterion of Guo-Lin [11], we constuct examples of unstable galaxy models of $f(E,L)$ and $f\left( E\right) \ $in which $f$ fails to be monotone in $E.$

Keywords:  Vlasov-Poisson, instability, galaxy model.
Mathematics Subject Classification:  Primary: 85A05; Secondary: 74A25.

Received: April 2013;      Revised: June 2013;      Available Online: November 2013.

 References