Communications in Mathematical Sciences

Volume 14 (2016)

Number 1

Convergence to the equilibrium state for a Bose–Einstein 1D Kac grazing limit model

Pages: 187 – 207



Radjesvarane Alexandre (Department of Mathematics and MOE-LSEC, Shanghai Jiao Tong University, Shanghai, China; and Arts et Métiers Paris Tech, Paris, France)

Jie Liao (School of Science, East China University of Science and Technology, Shanghai, China)

Chunjin Lin (Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China; and Department of Mathematics, College of Sciences, Hohai University, Nanjing, Jiangsu, China)


The convergence to the equilibrium of the solution of a quantum Kac grazing limit model for Bose–Einstein identical particles is studied. Using the relative entropy method and a detailed analysis of the entropy production, the exponential decay rate is obtained under suitable assumptions on the mass and energy of the initial data. These theoretical results are further illustrated through numerical simulations.


quantum Kac grazing limit model, relative entropy method, exponential decay

2010 Mathematics Subject Classification

35H10, 76P05

Published 16 September 2015