“…In fact, for the Boltzmann equation with cutoff hard potentials in the torus or even in a general bounded domain, Guo [49] developed a mathematical theory of global existence of small-amplitude L I x;v solutions by an L 2 -L I interplay method. Since then, there have been extensive generalizations and further developments of the Boltzmann global existence theory in the angular cutoff setting, for instance, [10,13,26,31,50,51,57,58,63,68]. Particularly, motivated by [26,49], Nishimura [68]…”