Lectures on the Energy Critical Nonlinear Wave Equation
Format:Paperback
Publisher:American Mathematical Society
Published:30th May '15
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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.
ISBN: 9781470420147
Dimensions: unknown
Weight: 314g
161 pages