Lectures on the energy critical nonlinear wave equation

Author(s)

• Kenig, Carlos E.
• Conference Board of the Mathematical Sciences

Bibliographic Information

Lectures on the energy critical nonlinear wave equation

Carlos E. Kenig

（Regional conference series in mathematics, no. 122）

Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c2015

Note

Published with support from the National Science Foundation

Bibliography: p. 157-161

"NSF-CBMS Regional Conference in Mathematical Sciences on the Energy Critical Nonlinear Wave Equation held at Kansas State University in June 2013."--T.p. verso

Description and Table of Contents

Description

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.

Table of Contents

The local theory of the Cauchy problem The ``road map'': The concentration compactness/rigidity theorem method for critical problems I The ``road map'': The concentration compactness/rigidity theorem method for critical problems II Properties of compact solutions and some more rigidity theorems, with applications to an extension of Theorem 2.6 Proof of the rigidity theorems Type II blow-up solutions Channels of energy and outer energy lower bounds Universal type II blow-up profiles Soliton resolution for radial solutions to (NLW), I Soliton resolution for radial solutions to (NLW), II Soliton resolution for radial solutions to (NLW), III Bibliography

by "Nielsen BookData"

Details

• NCID: BB18509687
• ISBN:
  • 9781470420147
• LCCN: 2015000062
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xiii, 161 p.
• Size: 26 cm
• Classification:
  • LCC : QA329.42
  • DC23 : 515/.353
• Subject Headings:
  • LCSH : Nonlinear partial differential operators
  • LCSH : Wave-motion, Theory of
• Parent Bibliography ID:
  • BA0000944X