On Vlasov-Manev equations. I. Foundations, properties, and nonglobal existence.

Details On Vlasov-Manev equations. I. Foundations, properties, and nonglobal existence. On Vlasov-Manev equations. I. Foundations, properties, and nonglobal existence.

Aug 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jsp....88..885b&link_type=abstract

J. Stat. Phys., Vol. 88, No. 3 - 4, p. 885 - 911

Physics

4

Stellar Dynamics: N-Body Problem

Scientific paper

The authors consider the classical stellar dynamic (Vlasov) equation with a so-called Manev correction (based on a pair potential γ/r+ɛ/r2). For the pure Manev potential γ = 0 they 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 ɛ/r2, 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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