# American Institute of Mathematical Sciences

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Cauchy problem on the Vlasov-Fokker-Planck equation coupled with the compressible Euler equations through the friction force
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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##### References:
 [1] Yulia O. Belyaeva, Björn Gebhard, Alexander L. Skubachevskii. A general way to confined stationary Vlasov-Poisson plasma configurations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021004 [2] Hai-Liang Li, Tong Yang, Mingying Zhong. Diffusion limit of the Vlasov-Poisson-Boltzmann system. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021003 [3] Hao Wang. Uniform stability estimate for the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 657-680. doi: 10.3934/dcds.2020292 [4] Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, 2021, 14 (1) : 149-174. doi: 10.3934/krm.2020052 [5] Yoshihisa Morita, Kunimochi Sakamoto. Turing type instability in a diffusion model with mass transport on the boundary. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3813-3836. doi: 10.3934/dcds.2020160 [6] Mingchao Zhao, You-Wei Wen, Michael Ng, Hongwei Li. A nonlocal low rank model for poisson noise removal. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021003 [7] Qing Li, Yaping Wu. Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3657-3682. doi: 10.3934/dcds.2020051 [8] Claude-Michel Brauner, Luca Lorenzi. Instability of free interfaces in premixed flame propagation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 575-596. doi: 10.3934/dcdss.2020363 [9] Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 [10] Jie Zhang, Yuping Duan, Yue Lu, Michael K. Ng, Huibin Chang. Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020071 [11] Denis Bonheure, Silvia Cingolani, Simone Secchi. Concentration phenomena for the Schrödinger-Poisson system in $\mathbb{R}^2$. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020447 [12] Li Cai, Fubao Zhang. The Brezis-Nirenberg type double critical problem for a class of Schrödinger-Poisson equations. Electronic Research Archive, , () : -. doi: 10.3934/era.2020125 [13] Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021003 [14] Juntao Sun, Tsung-fang Wu. The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021011 [15] Kazunori Matsui. Sharp consistency estimates for a pressure-Poisson problem with Stokes boundary value problems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1001-1015. doi: 10.3934/dcdss.2020380 [16] Simone Göttlich, Elisa Iacomini, Thomas Jung. Properties of the LWR model with time delay. Networks & Heterogeneous Media, 2020  doi: 10.3934/nhm.2020032 [17] Ténan Yeo. Stochastic and deterministic SIS patch model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021012 [18] M. Dambrine, B. Puig, G. Vallet. A mathematical model for marine dinoflagellates blooms. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 615-633. doi: 10.3934/dcdss.2020424 [19] Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457 [20] Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020464

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