Instability and Non-Uniqueness for the 2D Euler Equations, after M. Vishik : (ams-219) / Camillo De Lellis [and six others].

Format:

Book

Author/Creator:

De Lellis, Camillo, author.

Series:

Annals of mathematics studies ; Volume 215.

Annals of Mathematics Studies ; Volume 215

Language:

English

Subjects (All):

Differential equations, Partial.

Equations of motion.

Lagrange equations--Numerical solutions.

Lagrange equations.

Physical Description:

1 online resource (149 pages)

Edition:

First edition.

Place of Publication:

Princeton, New Jersey : Princeton University Press, [2024]

System Details:

Mode of access: World Wide Web.

Summary:

No detailed description available for "Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik".

Contents:

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.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Other Format:

Print version: Lellis, Camillo De Instability and Non-Uniqueness for the 2D Euler Equations, after M. Vishik

ISBN:

9780691257846

0691257841

OCLC:

1407283209