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This paper provides the first rigorous derivation of a binary-ternaryBoltzmann equation describing the kinetic properties of a dense hard-spheresgas, where particles undergo either binary or ternary instantaneousinteractions, while preserving momentum and energy. An important challenge weovercome in deriving this equation is related to providing a mathematicalframework that allows us to detect both binary and ternary interactions.Furthermore, this paper introduces new algebraic and geometric techniques inorder to eventually decouple binary and ternary interactions and understand theway they could succeed one another in time.

Rigorous derivation of a binary-ternary Boltzmann equation for a dense gas of hard spheres