The Hartree and Vlasov equations at positive density
Mathematical Physics
2019-10-22 v1 Analysis of PDEs
math.MP
Abstract
We consider the nonlinear Hartree and Vlasov equations around a translation-invariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. For both models, we consider time-dependent solutions which have a finite relative energy with respect to the reference translation-invariant state. We prove the convergence of the Hartree solutions to the Vlasov ones in a semi-classical limit and obtain as a by-product global well-posedness of the Vlasov equation in the (relative) energy space.
Cite
@article{arxiv.1910.09392,
title = {The Hartree and Vlasov equations at positive density},
author = {Mathieu Lewin and Julien Sabin},
journal= {arXiv preprint arXiv:1910.09392},
year = {2019}
}