We prove the convergence in any time interval of a point-particle approximation of the Vlasov equation by particles initially equally separated for a force in 1/|x|α, with α ≦ 1. We introduce discrete versions of the L ∞ norm and time averages of the force-field. The core of the proof is to show that these quantities are bounded and that consequently the minimal distance between particles in the phase space is bounded from below.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering