High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912483315286016 |
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| author | An, Gayoung Lee, Donghyun |
| author_facet | An, Gayoung Lee, Donghyun |
| contents | 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 $p=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09793 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations An, Gayoung Lee, Donghyun Analysis of PDEs 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 $p=2$. |
| title | High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2210.09793 |