Abstract
A functional approach, similar in spirit to that used by Bogoliubov in his studies of the BBGKY hierarchy, is used to derive the Smoluchowski equation from the Kramers-Chandrasekhar equation in the presence of a weak external magnetic field. A multiple time scales expansion is then used to solve the Kramers-Chandrasekhar equation as an initial value problem, thus allowing us to calculate the reduced initial data for the Smoluchowski equation. The relationship of the functional approach and the multiple time scales is discussed.
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