| 摘要 | 第1-6页 |
| Abstract | 第6-10页 |
| Chapter 1.Preface | 第10-13页 |
| §1.1 On the stability of a global supersonic conic shock of isothermal potential flow | 第10-11页 |
| §1.2 On the instability of a global supersonic conic shock of isothermal Euler flow | 第11-13页 |
| Chapter 2.Global and local multidimensional shock wave for the steady supersonic isothermal flow | 第13-65页 |
| §2.1. Introduction and main results | 第13-17页 |
| §2.2. Construction of approximate solution and its some related properties | 第17-23页 |
| §2.3. Local existence | 第23-44页 |
| ·Reformulate problem(2.1.7)with(2.1.8)-(2.1.10)under some transfor-mations | 第23-26页 |
| ·Construction of an approximate solution to the problem(2.3.10)with (2.3.11)-(2.3.12) | 第26-30页 |
| ·Construction of the iteration scheme and proof of local existence | 第30-44页 |
| 1. Preparation | 第30-33页 |
| 2. Notations | 第33-34页 |
| 3. Unique existence of an auxiliary problem | 第34-42页 |
| 4. Solvability of the problem(2.3.10)-(2.3.12) | 第42-44页 |
| §2.4. Reformulation of the nonlinear problem(2.1.7)together with(2.1.8)-(2.1.10) | 第44-47页 |
| §2.5. A first-order weighted energy estimate | 第47-57页 |
| §2.6. Higher-order weighted energy estimates | 第57-64页 |
| §2.7. Proof of Theorem 2.1.1 | 第64-65页 |
| Chapter 3. Instability of a global supersonic shock wave for the steady supersonic isothermal Euler flow | 第65-79页 |
| §3.1. Introduction and main results | 第65-68页 |
| §3.2. The analysis on the self-similar background solution | 第68-73页 |
| §3.3. Some crucial properties on globally stable supersonic conic waves | 第73-75页 |
| §3.4. Proof of Theorem 3.1.1 | 第75-79页 |
| Appendix A:Proofs of Lemma 2.4.2-Lemma 2.4.3 | 第79-81页 |
| Appendix B:Derivation of(3.10) | 第81-85页 |
| Appendix C:Basic computations | 第85-89页 |
| Bibliography | 第89-92页 |
| Acknowledgements | 第92-93页 |
| Finished papers during the program of my Ph.D study | 第93-94页 |
