Kinetic Description of Multiscale Phenomena

The Annual Kinetic FRG Meeting
May 23-26, 2011

Van Vleck Hall
Department of Mathematics
University of Wisconsin -Madison
Madison, WI 53706

Bose-Einstein condensation and a model for the Kompaneets equation

Prof. Hailiang Liu

Iowa State University

Abstract:  Recently there has been a wide interest in the Bose-Einstein condensation phenomena in the Kompaneets equation as a non-relativistic approximation model for photon diffusion, as well as in the quantum Boltzmann equation. In this talk I shall discuss the main issues involved with the Kompaneets equation, and present some new wellposedness results for a model with the spontaneous scattering term dropped, posed on a bounded interval (0, 1] subject to zero flux at x=1. For such a model problem, Bose-Einstein condensation is shown to form in finite time if initial photon number is above a threshold. Moreover, once a photon enters condensate it will stay there. This is a joint work with C.David Levermore and Robert Pego.