The grazing collision limit of Kac caricature of Bose-Einstein particles

Abstract

We discuss the grazing collision limit of certain kinetic models of Bose-Einstein particles obtained from a suitable modification of the one- dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in the limit a nonlinear Fokker-Planck equation which presents many similarities with the one introduced by Kaniadakis and Quarati in [13 ]. In order to do so, we perform a study of the moments of the solution. Moreover, as is typical in Maxwell models, we make an essential use of the Fourier version of the equation.

28 pages

References in corpus (2)

• Kinetics of Bose-Condensation
• Condensation of bosons in kinetic regime

Cited by in corpus (2)

• The Fokker-Planck equation for bosons in 2D: well-possedness and asymptotic analysis
• A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. Part I: Local existence of solutions