Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface vii
4. Acknowledgments xi
5. Introduction
6. 0.1 Idea of the proof 1
7. 0.2 Differences with Vishik’s work 6
8. 0.3 Further remarks 8
9. 1 General strategy: Background field and self-similar coordinates
10. 1.1 The initial velocity and the force 11
11. 1.2 The infinitely many solutions 16
12. 1.3 Logarithmic time scale and main Ansatz 18
13. 1.4 Linear theory 21
14. 1.5 Nonlinear theory 23
15. 1.6 Dependency tree 26
16. 2 Linear theory: Part I
17. Introduction 27
18. 2.1 Preliminaries 29
19. 2.2 Proof of Theorem 2.4 and proof of Theorem 2.1(a) 32
20. 2.3 Proof of Theorem 1.10: preliminary lemmas 34
21. 2.4 Proof of Theorem 1.10: conclusion 38
22. 3 Linear theory: Part II
23. Introduction 41
24. 3.1 Preliminaries 42
25. 3.2 The eigenvalue equation and the class 46
26. 3.3 A formal expansion 49
27. 3.4 Overview of the proof of Theorem 3.12 52
28. 3.5 ODE Lemmas 55
29. 3.6 Proof of Proposition 3.13 60
30. 3.7 Proof of Proposition 3.15: Part I 69
31. 3.8 Proof of Proposition 3.15: Part II 73
32. 3.9 Proof of Proposition 3.17 80
33. 3.10 Proof of Lemma 3.19 82
34. 4 Nonlinear theory
35. Introduction 87
36. 4.1 Proof of Proposition 4.2 89
37. 4.2 Proof of Lemma 4.3 92
38. 4.3 Proof of the baseline L² estimate 97
39. 4.4 Estimates on the first derivative 99
40. Appendix A. A more detailed spectral analysis
41. A.1 From Remark 3.3(i) to Remark 2.2(c) 105
42. A.2 Proof of Remark 3.3(i) 105
43. A.3 Proof of Theorem 3.4 111
44. A.4 Proof of Proposition A.4 112
45. Appendix B. Proofs of technical statements
46. B.1 Proof of Remark 0.2 121
47. B.2 Proof of Theorem 0.3 121
48. B.3 Proof of Proposition 1.5 123
49. B.4 Proof of Lemma 1.9 127
50. Bibliography 131
51. Index 135