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| 研究生： |
陳冠豪 Chen, Guan-Hao |
|---|---|
| 論文名稱： |
在歐式空間上動力傳輸方程和薛丁格方程的史特萊卡斯估計 On the Strichartz estimates for the kinetic transport equation and Schrodinger equation in R^d |
| 指導教授： |
江金城
Jiang, Jin-Cheng |
| 口試委員: |
蔡東和
Tsai, Dong-Ho 方永富 Fang, Yung-fu |
| 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： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 中文 |
| 論文頁數： | 16 |
| 中文關鍵詞： | 史特萊卡斯估計 、維格納變換 、動力傳輸方程 、薛丁格方程 |
| 外文關鍵詞： | Strichartz estimate, kinetic transport equation, Schrodinger equation, Wigner transform |
| 相關次數： | 點閱：26 下載：0 |
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韋格納變換可將薛丁格方程的解變換到動力傳輸方程的解，而逆韋格納變換則可將動力傳輸方程的解變換到薛丁格方程的解。而動力傳輸方程和薛丁格方程的解皆有色散估計。從色散估計可推導出史特萊卡斯估計。這篇研究主要結果是證明韋格納變換可以從傳輸方程的色散估計推到薛丁格方程的色散估計，而如果初始值皆大於零，則反方向也可以，但反方向在一般情況下卻不一定。
The Wigner transform can transform the solution of the Schrödinger equation into the solution of the kinetic transport equation, and the inverse Wigner transform can transform the solution of the kinetic transport equation into the solution of the Schrödinger equation. Both the solutions of the kinetic transport equation and the Schrödinger equation have dispersive estimates. The Strichartz estimates can be derived from the dispersive estimates. The main result of this study is to show that we can use the Wigner transform to derive the dispersive estimate of the Sch\"odinger equation from the dispersive estimate of the the kinetic transport equation, and if the initial values are all greater than zero, the reverse direction is also possible, but in general, the reverse direction is not always possible.
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