Microscopic derivation of Vlasov equations with singular potentials

Understand

The Vlasov-Poisson equation is a classical example of an effective equation which shall describe the coarse-grained time evolution of a system consisting of a large number of particles which interact by Coulomb or Newton's gravitational force.

• Although major progress concerning a rigorous justification of such an approach was made recently, there are still substantial steps necessary to obtain a completely convincing result.
• The main goal of this work is to yield further progress in this regard.
• \\ To this end, we consider on the one hand $N$-dependent forces $f^N$ (where $N$ shall denote the particle number) which converge pointwise to Coulomb or alternatively Newton`s gravitational force.