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Unstable and Stable Galaxy Models

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A Publisher's Erratum to this article was published on 15 April 2008

Abstract

To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models f 0(E), for which the distribution function f 0 depends on the particle energy E only. In the first part of the article, we derive the first sufficient criterion for linear instability of f 0(E) : f 0(E) is linearly unstable if the second-order operator

$$A_{0} \equiv-\Delta+4\pi\int f_{0}^{\prime}(E)\{I-{\mathcal{P}}\}dv$$

has a negative direction, where \({\mathcal{P}}\) is the projection onto the function space {g(E, L)}, L being the angular momentum [see the explicit formulae (29) and (28)]. In the second part of the article, we prove that for the important King model, the corresponding A 0 is positive definite. Such a positivity leads to the nonlinear stability of the King model under all spherically symmetric perturbations.

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Authors and Affiliations

  1. Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Yan Guo

  2. Mathematics Department, University of Missouri, Columbia, MO, 65211, USA

    Zhiwu Li

Authors
  1. Yan Guo
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  2. Zhiwu Li
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Correspondence to Yan Guo.

Additional information

Communicated by H. Spohn

An erratum to this article can be found at http://dx.doi.org/10.1007/s00220-008-0486-5

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Guo, Y., Li, Z. Unstable and Stable Galaxy Models. Commun. Math. Phys. 279, 789–813 (2008). https://doi.org/10.1007/s00220-008-0439-z

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  • DOI: https://doi.org/10.1007/s00220-008-0439-z

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