# American Institute of Mathematical Sciences

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December  2013, 6(4): 701-714. doi: 10.3934/krm.2013.6.701

## Unstable galaxy models

 1 School of Mathematical Sciences, Peking University, Beijing, 100871, China, China 2 Division of Applied Mathematics, Brown University, Providence, RI 02912, United States 3 School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States

Received  April 2013 Revised  June 2013 Published  November 2013

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 $E.$
Citation: Zhiyu Wang, Yan Guo, Zhiwu Lin, Pingwen Zhang. Unstable galaxy models. Kinetic & Related Models, 2013, 6 (4) : 701-714. doi: 10.3934/krm.2013.6.701
##### References:

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