Abstract
We consider the classical stellar dynamic (Vlasov) equation with a so-called Manev correction (based on a pair potential γ/r + ε/r 2). For the pure Manev potential γ = 0 we discuss both the continuous case and the N-body problem and show that global solutions will not exist if the initial energy is negative. Certain global solutions can be constructed from local ones by a transformation which is peculiar for the ε/r 2 law. Moreover, scaling arguments are used to show that Boltzmann collision terms are meaningful in conjunction with Manev force terms. In an appendix, a formal justification of the Manev correction based on the quasirelativistic Lagrangian formalism for the motion of a particle in a central force field is given.
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Bobylev, A.V., Dukes, P., Illner, R. et al. On Vlasov–Manev Equations. I: Foundations, Properties, and Nonglobal Existence. Journal of Statistical Physics 88, 885–911 (1997). https://doi.org/10.1023/B:JOSS.0000015177.60491.3c
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DOI: https://doi.org/10.1023/B:JOSS.0000015177.60491.3c