Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff
Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff
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DOI：
10.4171/aihpc/28
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Lingbing He;Yu-Long Zhou
中科院分区：
文献类型：
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作者：
Lingbing He;Yu-Long Zhou
给出了线性化玻尔兹曼碰撞算符及其方程从角截断到非角截断的渐近性的定量估计。一方面，这些结果揭示了由格拉德截断假设引起的双曲性质与长程相互作用引起的光滑性质之间的联系。另一方面，借助相空间中的局部化技术，我们观察到了渐近极限过程中的一些新现象。因此，我们对具有截断的碰撞算子不具有谱隙而不具有谱隙的性质在中等软势下不存在跳跃的问题给出了肯定的回答.
We give quantitative estimates on the asymptotics of the linearized Boltzmann collision operator and its associated equation from angular cutoff to non cutoff. On one hand, the results disclose the link between the hyperbolic property resulting from the Grad's cutoff assumption and the smoothing property due to the long-range interaction. On the other hand, with the help of the localization techniques in the phase space, we observe some new phenomenon in the asymptotic limit process. As a consequence, we give the affirmative answer to the question that there is no jump for the property that the collision operator with cutoff does not have the spectrum gap but the operator without cutoff does have for the moderate soft potentials.