We solve the Cauchy problem for the full non-linear homogeneous Boltzmann system of equations describing multi-component monatomic gas mixtures for binary interactions in three dimensions. More precisely, we show existence and uniqueness of the vector value solution by means of an existence theorem for ODE systems in Banach spaces under the transition probability rates assumption corresponding to hard potentials rates γ ∈ (0, 1], with a bounded angular section modeled by a bounded function of the scattering angle. The initial data for the vector valued solutions needs to be a vector of nonnegative positive measures that will have finite mass, momentum and strictly positive energy, as well as to have finite L 1 2+2γ (R 3 )-integrability corresponding to a sum across each species of 2 + 2γ-polynomial weighted norms depending in the corresponding mass fraction parameter for each species, referred as to the scalar polynomial moment of order 2 + 2γ. In addition there is no assumption on the finiteness of the initial system associated scalar entropy. This set of initial data assumptions allows for some of the species to be a singular mass initially.The existence and uniqueness proof relies on a new angular averaging lemma adjusted to vector values solution that yield a Povzner estimate with explicit constants that decay with the order of the corresponding scalar polynomial moment. In addition, such initial data yields global generation of such scalar polynomial moments at any order as well as their summability of moments to obtain estimates for corresponding scalar exponentially decaying high energy tails, referred as to scalar exponential moments associated to the system solution. Such scalar polynomial and exponential moments propagate as well.

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