Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 15-CNA-022 Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation C. David LevermoreDepartment of Mathematics University of Maryland College Park College Park, MD 20740 Hailiang LiuDepartment of Mathematics Iowa State University Ames, IA 50011 Robert L. PegoDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213rpego@andrew.cmu.eduAbstract: The Kompaneets equation describes a field of photons exchanging energy by Compton scattering with the free electrons of a homogeneous, isotropic, non-relativistic, thermal plasma. This paper strives to advance our understanding of how this equation captures the phenomenon of Bose-Einstein condensation through the study of a model equation. For this model we prove existence and uniqueness theorems for global weak solutions. In some cases a Bose-Einstein condensate will form in finite time, and we show that it will continue to gain photons forever afterwards. Moreover we show that every solution approaches a stationary solution for large time. Key tools include a universal super solution, a one-sided Oleinik type inequality, and an $L^1$ contraction. Get the paper in its entirety as  15-CNA-022.pdf