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arXiv · 1910.09392

The Hartree and Vlasov equations at positive density

Mathieu Lewin·Julien Sabin
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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.

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Mathieu Lewin, Julien Sabin. 2019-10-21. The Hartree and Vlasov equations at positive density. https://arxiv.org/abs/1910.09392

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