Lectures on the Energy Critical Nonlinear Wave Equation (Cbms Regional Conference Series in Mathematics) - Softcover

Kenig, Carlos E.

Softcover

ISBN 10: 1470420147 ISBN 13: 9781470420147

Publisher: American Mathematical Society, 2015

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.

About this title

About the Author

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2015
• Language: English
• ISBN 10: 1470420147
• ISBN 13: 9781470420147
• Binding: Paperback
• Number of pages: 161