论文标题
非弹性和多物种混合物玻尔兹曼方程的高速尾巴
High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations
论文作者
论文摘要
我们研究了$ v \ in \ mathbb {r} _ {v}^d $ in $ v \ in $ v \ of $ v \ of $ v \ to boltzmann方程的高速尾。首先，在中等软势的情况下，我们考虑具有非Cutoff碰撞内核的空间均匀非弹性玻尔兹曼方程。我们还研究了空间均匀的混合物玻尔兹曼方程：对于具有适度柔软电势的非cutoff碰撞内核，且具有硬势的截止碰撞内核。在非弹性非弹性玻尔兹曼的情况下，我们获得了 \ [ f（t，v）\ geq a（t）e^{ - b（t）| v |^p}，\ quad 2 <p <6.213 \] 通过扩展取消引理并扩散引理并假设在c^{\ infty} $中假设$ f \。对于混合物类型的Boltzmann方程式，我们证明Maxwellian $ P = 2 $。
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 $p=2$.
