A New Approach to the Creation and Propagation of Exponential Moments in the Boltzmann Equation
A New Approach to the Creation and Propagation of Exponential Moments in the Boltzmann Equation
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DOI：
10.1080/03605302.2012.715707
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发表时间：
2012-03
影响因子：
1.9
通讯作者：
R. Alonso;J. Cañizo;I. Gamba;C. Mouhot
中科院分区：
文献类型：
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作者：
R. Alonso;J. Cañizo;I. Gamba;C. Mouhot
我们研究了空间齐次d维Boltzmann方程解的指数矩的产生和传播。特别地，当碰撞核具有以下形式时：|v − v *| β B（cos（θ）），对于β ∈（0，2]，其中cos（θ）=| v − v *| −1（v − v *）·σ和σ ∈𝕊 d−1，并假设经典的截断条件B（cos（θ））在d−1中可积𝕊，证明了存在a > 0使得权矩exp（amin {t，1}| v| β）对于t > 0是有限的，其中α只取决于碰撞核和初始质量和能量。基于一个单微分不等式，提出了一种新的证明含时指数矩的方法。
We study the creation and propagation of exponential moments of solutions to the spatially homogeneous d-dimensional Boltzmann equation. In particular, when the collision kernel is of the form |v − v *|β b(cos (θ)) for β ∈ (0, 2] with cos (θ) = |v − v *|−1(v − v *)·σ and σ ∈ 𝕊 d−1, and assuming the classical cut-off condition b(cos (θ)) integrable in 𝕊 d−1, we prove that there exists a > 0 such that moments with weight exp (amin {t, 1}|v|β) are finite for t > 0, where a only depends on the collision kernel and the initial mass and energy. We propose a novel method of proof based on a single differential inequality for the exponential moment with time-dependent coefficients.