Lectures on the Energy Critical Nonlinear Wave Equation
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A01=Carlos E. Kenig
Author_Carlos E. Kenig
Category=PBKJ
Category=PBW
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Product details
- ISBN 9781470420147
- Weight: 314g
- Dimensions: 178 x 254mm
- Publication Date: 30 May 2015
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
Carlos E. Kenig, University of Chicago, IL, USA.
