Lectures on the Energy Critical Nonlinear Wave Equation
Format: Paperback
ISBN13: 9781470420147
Paperback|9781470420147
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Overview
This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the ``concentration-compactness/rigidity theorem method'' introduced by C. Kenig and F. Merle. This approach has become the canonical method for the study of the ``global regularity and well-posedness'' conjecture (defocusing case) and the ``ground-state'' conjecture (focusing case) in critical dispersive problems.
The second part of the monograph describes the ``channel of energy'' method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation.
It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations.
The second part of the monograph describes the ``channel of energy'' method, introduced by T. Duyckaerts, C. Kenig, and F. Merle, to study soliton resolution for nonlinear wave equations. This culminates in a presentation of the proof of the soliton resolution conjecture, for the three-dimensional radial focusing energy critical wave equation.
It is the intent that the results described in this book will be a model for what to strive for in the study of other nonlinear dispersive equations.
| ISBN-13 | 9781470420147 |
|---|---|
| ISBN-10 | 1470420147 |
| Weight | 0.70 Pounds |
| Dimensions | 7.00 x 0.50 x 10.25 In |
| List Price | $52.00 |
| Format | Paperback |
|---|---|
| Language | English |
| Pages | 162 pages |
| Publisher | American Mathematical Society |
| Published On | 2015-05-30 |
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