High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations

Abstract

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 $p=2$.

Cited by in corpus (1)

• Quantitative pointwise estimates of the cooling process for inelastic Boltzmann equation