Series: CBMS Regional Conference Series in Mathematics. Num Pages: 161 pages. BIC Classification: PBKJ; PBW. Category: (P) Professional & Vocational. Dimension: 254 x 178. Weight in Grams: 525. . 2015. Paperback. . . . .

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Bibliographic Details

Title: Lectures on the Energy Critical Nonlinear Wave Equation
Publisher: American Mathematical Society
Publication Date: 2015
Language: English
ISBN 10: 1470420147
ISBN 13: 9781470420147
Binding: Soft cover
Condition: New

About this title

Synopsis

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.

About the Author

Carlos E. Kenig, University of Chicago, IL, USA.

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