Large-Time Behavior of Solutions for the Boltzmann Equation with Hard potentials
Large-Time Behavior of Solutions for the Boltzmann Equation with Hard potentials
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DOI：
10.1007/s00220-006-0108-z
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发表时间：
2006-09
影响因子：
2.4
通讯作者：
Ming-Yi Lee;Tai-Ping Liu;Shih-Hsien Yu
中科院分区：
文献类型：
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作者：
Ming-Yi Lee;Tai-Ping Liu;Shih-Hsien Yu
研究了具有格拉德角截断的硬势模型的一维Boltzmann方程解的定量行为。我们的结果推广了[5]中关于硬球模型的结果。硬球模型和硬势模型的主要区别在于碰撞频率的指数。这引起了新的波动现象，特别是波的次指数行为。与硬球模型不同，硬势模型的Fourier算符谱在η中是非解析的。因此，复解析法反演傅里叶变换是不适用的，我们需要使用真实的分析方法在流体波的估计。我们设计了一个新的加权能量函数来解释波的次指数行为。
We study the quantitative behavior of the solutions of the one-dimensional Boltzmann equation for hard potential models with Grad’s angular cutoff. Our results generalize those of [5] for hard sphere models. The main difference between hard sphere and hard potential models is in the exponent of the collision frequency. This gives rise to new wave phenomena, particularly the sub-exponential behavior of waves. Unlike the hard sphere models, the spectrum of the Fourier operatoris non-analytic in η for hard potential models. Thus the complex analytic methods for inverting the Fourier transform are not applicable and we need to use the real analytic method in the estimates of the fluidlike waves. We devise a new weighted energy function to account for the sub-exponential behavior of waves.