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arXiv · 1512.06780

Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation

C. David Levermore·Hailiang Liu·Robert L. Pego
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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.

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C. David Levermore, Hailiang Liu, Robert L. Pego. 2015-12-22. Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. https://arxiv.org/abs/1512.06780

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