On Pseudoconformal Blow-Up Solutions to the Self-Dual Chern-Simons-Schrödinger Equation : Existence, Uniqueness, and Instability / Kihyun Kim and Soonsik Kwon.

Format:

Book

Author/Creator:

Kim, Kihyun, author.

Kwon, Soonsik, author.

Series:

Memoirs of the American Mathematical Society ; Volume 284.

Memoirs of the American Mathematical Society Series ; Volume 284

Language:

English

Subjects (All):

Differential equations, Nonlinear.

Blowing up (Algebraic geometry).

Physical Description:

1 online resource (140 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

View the abstract.

Contents:

Cover

Title page

Chapter 1. Introduction

1.1. Covariant formulation

1.2. Coulomb gauge and equivariance reduction

1.3. Static solution for the self-dual (CSS)

1.4. Pseudoconformal blow-up solutions and main results

1.5. Strategy of the proof

Organization of the paper

Acknowledgments

Chapter 2. Notations and preliminaries

2.1. Basic notations

2.2. Equivariant Sobolev spaces

2.3. Time maximal functions

2.4. Decomposition of nonlinearity and duality estimates

2.5. Dynamic rescaling

2.6. Local theory of (CSS) under equivariance

Chapter 3. Linearization of (CSS) under equivariance

3.1. Linearization of Bogomol'nyi operator

3.2. Linearization of (CSS)

3.3. Algebraic relations, solvability, and coercivity of ℒ_{ }

Chapter 4. Profile ^{( )}

4.1. Role of pseudoconformal phase

4.2. A hint to rotational instability

4.3. Construction of ^{( )}

Chapter 5. Setup for modulation analysis

5.1. Corrections from the interaction between _{ }^{♯} and

5.2. Evolution of

5.3. Choice of modulation parameters

5.4. Reduction of Theorems 1.1 and 1.3 to the main bootstrap Lemma 5.3

Chapter 6. Proof of bootstrap Lemma 5.3

6.1. Estimates of ̃ _{ _{ }^{( )}, ^{♭}}

6.2. Estimates of _{ ^{♭}- ^{♭}}, ℒ_{ ^{♭}}-ℒ_{ _{ }^{( )}}, and ℒ_{ _{ }^{( )}}-ℒ_{ }

6.3. Modulation estimates

6.4. ²-bound of

6.5. Lyapunov/virial functional

6.6. Closing the bootstrap

Chapter 7. Conditional uniqueness

7.1. A priori estimates on ₁ and ₂

7.2. Estimates of

7.3. Lyapunov/virial functional

7.4. Proof of conditional uniqueness

Appendix A. Equivariant Sobolev spaces

A.1. Smooth equivariant functions

A.2. Equivariant Sobolev spaces

Appendix B. Equivariant local theory

Bibliography

Back Cover.

Notes:

Description based on print version record.

Includes bibliographical references.

ISBN:

1-4704-7447-6