Volume: 122; 2015; 161 pp; Softcover
MSC: Primary 35;
Print ISBN: 978-1-4704-2014-7
Product Code: CBMS/122
List Price: $52.00
AMS Member Price: $41.60
MAA Member Price: $46.80
Electronic ISBN: 978-1-4704-2273-8
Product Code: CBMS/122.E
List Price: $49.00
AMS Member Price: $39.20
MAA Member Price: $44.10
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Supplemental Materials
Lectures on the Energy Critical Nonlinear Wave Equation
Share this pageCarlos E. Kenig
A co-publication of the AMS and CBMS
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.
A co-publication of the AMS and CBMS.
Readership
Graduate students and research mathematicians interested in nonlinear wave equations.
Table of Contents
Table of Contents
Lectures on the Energy Critical Nonlinear Wave Equation
- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Introduction vii8 free
- The local theory of the Cauchy problem 116 free
- The “road map”: The concentration compactness/rigidity theorem method for critical problems I 1732
- The “road map”: The concentration compactness/rigidity theorem method for critical problems II 3146
- Properties of compact solutions and some more rigidity theorems, with applications to an extension of Theorem 2.6 4560
- Proof of the rigidity theorems 6984
- Type II blow-up solutions 8196
- Channels of energy and outer energy lower bounds 101116
- Universal type II blow-up profiles 109124
- Soliton resolution for radial solutions to (NLW), I 121136
- Soliton resolution for radial solutions to (NLW), II 135150
- Soliton resolution for radial solutions to (NLW), III 145160
- Bibliography 157172
- Back Cover Back Cover1177