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

Thibaut Allemand (1) , Giuseppe Toscani (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Dipartimento di matematica F. Casorati

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.

Mots clés: grazing collision; kinetic; Kac equation; Fokker-Planck equation

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Thibaut Allemand, Giuseppe Toscani. The grazing collision limit of Kac caricature of Bose-Einstein particles. Asymptotic Analysis, 2011, 72 (3-4), pp.201-229. ⟨10.3233/ASY-2011-1031⟩. ⟨hal-00367518v3⟩