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Unstable and Stable Galaxy Models
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 , for which the distribution function
depends on the particle energy only. In the first part of the article, we
derive the first sufficient criterion for linear instability of
is linearly unstable if the second-order operator has a
negative direction, where is the projection onto the function
space being the angular momentum [see the explicit formula
(\ref{A0-radial})]. In the second part of the article, we prove that for the
important King model, the corresponding is positive definite. Such a
positivity leads to the nonlinear stability of the King model under all
spherically symmetric perturbations.Comment: to appear in Comm. Math. Phy
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