Publication 15-CNA-022
Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation
C. David Levermore
Department of Mathematics
University of Maryland College Park
College Park, MD 20740
lvrmr@umd.edu
Hailiang Liu
Department of Mathematics
Iowa State University
Ames, IA 50011
hliu@iastate.edu
Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rpego@andrew.cmu.edu
Abstract: 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
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