| 关于Boltzmann方程的空间均匀的ES模型 |
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| 引用本文： | 张显文,胡适耕,张诚坚. 关于Boltzmann方程的空间均匀的ES模型[J]. 应用数学, 2006, 19(2): 426-432 |
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| 作者姓名： | 张显文 胡适耕 张诚坚 |
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| 作者单位： | 华中科技大学数学系,武汉,430074 |
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| 摘 要： | 在Prandtl数Pr∈[2/3,∞)的情况下,我们讨论了Boltzmann方程的空间均匀的椭圆统计模型.首先,我们建立了解的存在唯一性.其次,我们证明了该解收敛到平衡态并给出了其Maxwell分布型的下界估计.最后,我们给出了熵等式从而证明了该方程的熵是衰减的.
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| 关 键 词： | Boltzmann方程 椭圆统计模型 长时间渐近行为 Maxwell分布型下界 |
| 文章编号： | 1001-9847(2006)02-0426-07 |
| 收稿时间： | 2005-09-09 |
| 修稿时间： | 2005-09-09 |
On the Spatially Homogeneous ES Model of the Boltzmann Equation |
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| ZHANG Xian-wen,HU Shi-geng,ZHANG Cheng-jian. On the Spatially Homogeneous ES Model of the Boltzmann Equation[J]. Mathematica Applicata, 2006, 19(2): 426-432 |
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| Authors: | ZHANG Xian-wen HU Shi-geng ZHANG Cheng-jian |
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| Affiliation: | Department of Mathematics, Huazhong University of Science and Technology, Hubei Wuban 430074,China |
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| Abstract: | We discuss the solution properties of the spatially homogeneous ellipsoidal statistical model (ES model) of the Boltzmann equation with Prandtl number Pr ∈ [2/3,∞). First, we establish the existence and uniqueness result. Second, the trend towards equilibrium and the Maxwellian lower bound estimates of the solution are established. Finally, we prove the entropy identity and obtain dissipation of the entropy of this equation. |
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| Keywords: | Boltzmann equation ES model Long-time behavior Maxwellian lower bound |
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