The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive estimates
Arnold, Anton ; Dhamo, Elidon ; Manzini, Chiara
arXiv, 0505385 / Harvested from arXiv
Text on arXiv
This paper is concerned with the Wigner-Poisson-Fokker-Planck system, a kinetic evolution equation for an open quantum system with a non-linear Hartree potential. Existence, uniqueness and regularity of global solutions to the Cauchy problem in 3 dimensions are established. The analysis is carried out in a weighted L^2-space, such that the linear quantum Fokker-Planck operator generates a dissipative semigroup.The non-linear potential can be controled by using the parabolic regularization of the system. The main technical difficulty for establishing global-in-time solutions is to derive a-priori estimates on the electric field:Inspired by a strategy for the classical Vlasov-Fokker-Planck equation, we exploit dispersive effects of the free transport operator. As a ``by-product'' we also derive a new a-priori estimate on the field in the Wigner-Poisson equation.
Publié le : 2005-05-18
Classification:  Mathematics - Analysis of PDEs,  Mathematical Physics,  35A05, 35K55, 35Q40, 47B44, 81Q99, 81S30, 82D37 
@article{0505385,
     author = {Arnold, Anton and Dhamo, Elidon and Manzini, Chiara},
     title = {The Wigner-Poisson-Fokker-Planck system: global-in-time solution and
  dispersive estimates},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505385}
}

Arnold, Anton; Dhamo, Elidon; Manzini, Chiara. The Wigner-Poisson-Fokker-Planck system: global-in-time solution and
  dispersive estimates. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505385/