Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction

Autor:	Hadama, Sonae, Hong, Younghun
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form $\gamma_f=f(-\Delta)$ representing quantum states of infinitely many particles. In this article, we consider the time evolution of perturbations from a large class of such steady states via the three-dimensional NLH. We prove that if the interaction potential $w$ has finite measure and initial states have finite relative entropy, then solutions preserve the relative free energy, and they exist globally in time. This result extends the important work of Lewin and Sabin [arXiv:1310.0603] to singular interaction cases. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.06730 Zobrazit plný text záznamu View this record from Arxiv