We study high-velocity tails of some homogeneous Boltzmann equations on $v \in \mathbb{ R}_{ v}^d$. First, we consider spatially homogeneous inelastic Boltzmann equation with noncutoff collision kernel, in the case of moderately soft potentials. We also study spatially homogeneous mixture Boltzmann equations : for both noncutoff collision kernel with moderately soft potentials and cutoff collision kernel with hard potentials. In the case of noncutoff inelastic Boltzmann, we obtain \[ f(t,v) \geq a(t) e^{ -b(t)|v|^p}, \quad 2 < p < 6.213 \] by extending Cancellation lemma and spreading lemma and assuming $f\in C^{ \infty}$. For the Mixture type Boltzmann equations, we prove Maxwellian $p=2$.
Categories: math.AP