# Stable Ground States and Self-Similar Blow-Up Solutions for the Gravitational Vlasov-Manev System

@article{Lemou2012StableGS,
title={Stable Ground States and Self-Similar Blow-Up Solutions for the Gravitational Vlasov-Manev System},
author={Mohammed Lemou and Florian M{\'e}hats and Cyril Rigault},
journal={SIAM J. Math. Anal.},
year={2012},
volume={44},
pages={3928-3968}
}
• Published 1 June 2010
• Mathematics, Physics, Computer Science
• SIAM J. Math. Anal.
In this work, we study the orbital stability of steady states and the existence of blow-up self-similar solutions to the so-called Vlasov-Manev (VM) system. This system is a kinetic model which has a similar Vlasov structure as the classical Vlasov-Poisson system, but is coupled to a potential in $-1/r- 1/r^2$ (Manev potential) instead of the usual gravitational potential in $-1/r$, and in particular the potential field does not satisfy a Poisson equation but a fractional-Laplacian equation. We…
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