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研究生： 許祐承
Hsu, Yu-Cheng
論文名稱： 回顧波茲曼方程的能量估計法
The review of energy method for Boltzmann equation
指導教授： 江金城
JIANG, JIN-CHENG
口試委員: 蔡東和
TSAI, DONG-HO
李明憶
LI, MING-YI
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2020
畢業學年度： 108
語文別： 中文
論文頁數： 61
中文關鍵詞： 波茲曼方程 、H定理 、麥克斯威爾狀態 、巨觀-微觀分解
外文關鍵詞： Boltzmann equation, H-Theorem, Maxwellian state, Macro-micro decomposition
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    • 在這篇論文中，我們複習波茲曼方程的巨觀-微觀分解,並利用此分解得出能量估計法。我們利用能量估計法來研究全域麥克斯威爾狀態的時間漸進，非線性穩定性問題。

    In this paper, we review the macro-micro decomposition of the Boltzmann equation which yields the energy estimate method.We will apply this method to study the problem of time-asymptotic, non-linear stability of the global Maxwellian state.

    1.Introduction...1 1.1 Setting...1 1.2 Linearised Collision Operator...4 1.3 The Conservation Laws...6 2.H-Theorem...11 2.1 Microscopic version of H-theorem...11 2.2 Boltzmann inequality...12 2.3 Macroscopic version of H-theorem...14 3.Nonlinear stability of a Maxwellian state...29 3.1 Lower order energy estimates of the fluid variables...29 3.2 Lower order energy estimates of the non-fluid variables...34 3.3 Higher order energy estimates...43 Appendices...54 I Some Calculations...54 II Collision Operator...56 III The proof of estimate on Q({\bf G},{\bf G})...58 Reference...60

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