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Lectures on the Energy Critical Nonlinear Wave Equation

Carlos E. Kenig University of Chicago, Chicago, IL
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-1-4704-2014-7
Product Code: CBMS/122
161 pp
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-2273-8 Product Code: CBMS/122.E 161 pp List Price:$49.00
MAA Member Price: $44.10 AMS Member Price:$39.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view Lectures on the Energy Critical Nonlinear Wave Equation Carlos E. Kenig University of Chicago, Chicago, IL A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-1-4704-2014-7 Product Code: CBMS/122 161 pp  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-2273-8 Product Code: CBMS/122.E 161 pp
 List Price: $49.00 MAA Member Price:$44.10 AMS Member Price: $39.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$78.00
MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1222015
MSC: Primary 35;

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.

Graduate students and research mathematicians interested in nonlinear wave equations.

• Chapters
• 1. The local theory of the Cauchy problem
• 2. The “road map”: The concentration compactness/rigidity theorem method for critical problems I
• 3. The “road map”: The concentration compactness/rigidity theorem method for critical problems II
• 4. Properties of compact solutions and some more rigidity theorems, with applications to an extension of Theorem 2.6
• 5. Proof of the rigidity theorems
• 6. Type II blow-up solutions
• 7. Channels of energy and outer energy lower bounds
• 8. Universal type II blow-up profiles
• 9. Soliton resolution for radial solutions to (NLW), I
• 10. Soliton resolution for radial solutions to (NLW), II
• 11. Soliton resolution for radial solutions to (NLW), III

• Request Review Copy
Volume: 1222015
MSC: Primary 35;

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.

Graduate students and research mathematicians interested in nonlinear wave equations.

• Chapters
• 1. The local theory of the Cauchy problem
• 2. The “road map”: The concentration compactness/rigidity theorem method for critical problems I
• 3. The “road map”: The concentration compactness/rigidity theorem method for critical problems II
• 4. Properties of compact solutions and some more rigidity theorems, with applications to an extension of Theorem 2.6
• 5. Proof of the rigidity theorems
• 6. Type II blow-up solutions
• 7. Channels of energy and outer energy lower bounds
• 8. Universal type II blow-up profiles
• 9. Soliton resolution for radial solutions to (NLW), I
• 10. Soliton resolution for radial solutions to (NLW), II
• 11. Soliton resolution for radial solutions to (NLW), III
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