In this talk, I will present our recent results on space-time structure of nonlinear Boltzmann equation with hard and soft potentials. The key ingredients in our approach are various versions of Mixture Lemma, which reveal that the combined effect of transport and collision will bring regularity and decay in both space and velocity variables as good as one pleases. The solution operator is thus decomposed into particle-like and fluid-like parts, and the nonlinear problem is completed by a coupled integral equation. The duality between particle part and fluid part will also be discussed.

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