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Publication 132

Global Dynamics of Bose-Einstein Condensation for a Model of the Kompaneets Equation


C. D. Levermore
Department of Mathematics
University of Maryland College Park
College Park, MD 20740

H. Liu
Department of Mathematics
Iowa State University
Ames, IA 50011

CMURobert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

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.
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