The Hartree and Vlasov equations at positive density
Abstract
We consider the nonlinear Hartree and Vlasov equations around a translationinvariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. For both models, we consider timedependent solutions which have a finite relative energy with respect to the reference translationinvariant state. We prove the convergence of the Hartree solutions to the Vlasov ones in a semiclassical limit and obtain as a byproduct global wellposedness of the Vlasov equation in the (relative) energy space.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 DOI:
 10.48550/arXiv.1910.09392
 arXiv:
 arXiv:1910.09392
 Bibcode:
 2019arXiv191009392L
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs