On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence

Autor:	He, Ling-Bing, Lu, Xuguang, Pulvirenti, Mario
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-021-04029-7
Popis:	It is expected in physics that the homogeneous quantum Boltzmann equation with Fermi-Dirac or Bose-Einstein statistics and with Maxwell-Boltzmann operator (neglecting effect of the statistics) for the weak coupled gases will converge to the homogeneous Fokker-Planck-Landau equation as the Planck constant $\hbar$ tends to zero. In this paper and the upcoming work \cite{HLP2}, we will provide a mathematical justification on this semi-classical limit. Key ingredients into the proofs are the new framework to catch the {\it weak projection gradient}, which is motivated by Villani \cite{V1} to identify the $H$-solution for Fokker-Planck-Landau equation, and the symmetric structure inside the cubic terms of the collision operators. Comment: 57 pages with an Appendix
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.01529 Zobrazit plný text záznamu View this record from Arxiv