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

  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.},
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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