A rigorous derivation of Smoluchowski's equation in the moderate limit

Details A rigorous derivation of Smoluchowski's equation in the moderate limit A rigorous derivation of Smoluchowski's equation in the moderate limit

2003-04-08

arxiv.org/abs/math/0304107v1

Stoch. An. Appl. 22(1), 113-142 (2004)

Mathematics

Probability

19 pages, to appear in Stoch. An. Appl

Scientific paper

Smoluchowski's equation is a macroscopic description of a many particle system with coagulation and shattering interactions. We give a microscopic model of the system from which we derive this equation rigorously. Provided the existence of a unique and sufficiently regular solution of Smoluchowski's equation, we prove the law of large numbers for the empirical processes. In contrast to previous derivations we assume a moderate scaling of the particle interaction, enabling us to estimate the critical fluctuation terms by using martingale inequalities. This approach can be justified in the regime of high temperatures and particle densities, which is of special interest in astrophysical studies and where previous derivations do not apply.

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