Global well-posedness of a binary–ternary Boltzmann equation

In this paper we show global well-posedness near vacuum for the binary-ternary Boltzmann equation. The equation provides a correction term to classical equation, taking into account both binary and ternary interactions of particles, may serve as more accurate description model denser gases in non-equilibrium. Well-posedness and, independently, purely follow special cases. To prove well-posedness, use Kaniel-Shinbrot iteration related work approximate solution nonlinear by monotone sequences supersolutions subsolutions. This analysis required establishing new convolution type estimates control contribution collisional operator model. We that allows consideration softer potentials than one operator, consequently our preserves all properties solution. These results are novel operators monoatomic with either hard or soft interactions.