Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik: (AMS-219) (Annals of Mathematics Studies, 219)

Cover
Contents
Preface
Acknowledgments
Introduction
	0.1 Idea of the proof
	0.2 Differences with Vishik\'s work
	0.3 Further remarks
Chapter 1. General strategy: Background field and self-similar coordinates
	1.1 The initial velocity and the force
	1.2 The infinitely many solutions
	1.3 Logarithmic time scale and main Ansatz
	1.4 Linear theory
	1.5 Nonlinear theory
	1.6 Dependency tree
Chapter 2. Linear theory: Part I
	2.1 Preliminaries
	2.2 Proof of Theorem 2.4 and proof of Theorem 2.1(a)
	2.3 Proof of Theorem 1.10: preliminary lemmas
	2.4 Proof of Theorem 1.10: conclusion
Chapter 3. Linear theory: Part II
	3.1 Preliminaries
	3.2 The eigenvalue equation and the class C
	3.3 A formal expansion
	3.4 Overview of the proof of Theorem 3.12
	3.5 ODE Lemmas
	3.6 Proof of Proposition 3.13
	3.7 Proof of Proposition 3.15: Part I
	3.8 Proof of Proposition 3.15: Part II
	3.9 Proof of Proposition 3.17
	3.10 Proof of Lemma 3.19
Chapter 4. Nonlinear theory
	4.1 Proof of Proposition 4.2
	4.2 Proof of Lemma 4.3
	4.3 Proof of the baseline L2 estimate
	4.4 Estimates on the first derivative
Appendix A
	A.1 From Remark 3.3(i) to Remark 2.2(c)
	A.2 Proof of Remark 3.3(i)
	A.3 Proof of Theorem 3.4
	A.4 Proof of Proposition A.4
Appendix B
	B.1 Proof of Remark 0.2
	B.2 Proof of Theorem 0.3
	B.3 Proof of Proposition 1.5
	B.4 Proof of Lemma 1.9
Bibliography
Index