One of the first profound analysis about the solutions of the Boltzmann Equation was given by DiPerna and Lions in the late 1980s. You can find one of their main papers here: http://www.jstor.org/discover/10.2307/1971423?uid=3737528&uid=2&uid=4&sid=21102076873573
If you do not have access to the paper then use this link: http://www.4shared.com/office/eeIqgvxB/MathematicsOn_the_Cauchy_Probl.html
I was reading through this and similar papers and one of the things I do not understand is the interpretation of the solution. The paper delivers more or less a proof for the existence of a global solution of the Boltzmann Equation, but what can we do with it? If you have an idea how to interpret it I would be very thankful.
P.S: I put a question about the proof of one of the Lemmas on https://mathoverflow.net/questions/132871/cauchy-problem-for-boltzmann-equations