Global L¹ theory and regularity for the 3D nonlinear Wigner–Poisson–Fokker–Planck system

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• 作者：Cañ ; izo ; José ; A. ; Ló ; pez ; José ; Luis ; Nieto ; Juan
• 关键词：Open quantum system ; Wigner equation ; Fokker&ndash ; Planck operator ; Global solution ; Husimi transform ; Elliptic regularization
• 刊名：Journal of Differential Equations
• 出版年：2004
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：April 10, 2004
• 卷：198
• 期：2
• 页码：356-373
• 文件大小：280 K

摘要

A global existence, uniqueness and regularity theorem is proved for the simplest Markovian Wigner–Poisson–Fokker–Planck model incorporating friction and dissipation mechanisms. The proof relies on Green function and energy estimates under mild formulation, making essential use of the Husimi function and the elliptic regularization of the Fokker–Planck operator.