Abstract
In Chapter 2 we gave a formal derivation of the Boltzmann equation from the basic laws of mechanics. In particular, we introduced the Liouville equation, the BBGKY hierarchy, the Boltzmann hierarchy, and the Boltzmann equation, and we discussed the assumptions that allowed us to make the transitions from each of those to the next. The objective of this chapter is to do all these steps rigocrously, wherever possible. In particular, our discussion will lead to a rigorous validity and existence result for the Boltzmann equation, locally for a general situation and globally for a rare gas cloud in vacuum.
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Cercignani, C., Illner, R., Pulvirenti, M. (1994). Rigorous Validity of the Boltzmann Equation. In: The Mathematical Theory of Dilute Gases. Applied Mathematical Sciences, vol 106. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8524-8_5
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DOI: https://doi.org/10.1007/978-1-4419-8524-8_5
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