On Vlasov-Manev equations .1. Foundations, properties, and nonglobal existence

We consider the classical stellar dynamic (Vlasov) equation with a so-called Manev correction (based on a pair potential gamma/r + epsilon/r(2)). For the pure Manev potential gamma = 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 epsilon/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.