Friday, July 12, 2013

1307.2999 (Niklas Boers et al.)

On Mean Field Limits for Dynamical Systems    [PDF]

Niklas Boers, Peter Pickl, Detlef Dürr
Recently, a new strategy has been invented to prove propagation of molecular chaos in mean-field situations, establishing mean-field equations (Hatree or Gross-Pitaevskii) for microscopic many-particle quantum dynamics. It relies on a Gronwall estimate for a suitably defined measure of independence. We extend the method to classical systems and apply it to prove Vlasov-type limits for classical many-particle systems. We prove $L^1$-convergence and obtain from that existence and uniqueness of strong solutions of the Vlasov-type equations.
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