Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails

Details Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails

2006-08-17

arxiv.org/abs/cond-mat/0608397v1

Journal of Statistical Physics, Online available since April 2006

Physics

Condensed Matter

Statistical Mechanics

20 pages

Scientific paper

10.1007/s10955-006-9044-8

We consider the Boltzmann equations for mixtures ofMaxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that power like tails can appear not just for granular particles (Maxwell models are far from reality in this case), but also in the system of particles interacting in accordance with laws of classical mechanics. In addition, non-existence of positive self-similar solutions with finite moments of any order is proven for a wide class of Maxwell models.

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