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Advances in AnalysisThe Legacy of Elias M. Stein$
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Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Print publication date: 2014

Print ISBN-13: 9780691159416

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159416.001.0001

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The Energy Critical Wave Equation in 3D

The Energy Critical Wave Equation in 3D

Chapter:
(p.215) Chapter Nine The Energy Critical Wave Equation in 3D
Source:
Advances in Analysis
Author(s):

Carlos Kenig

, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691159416.003.0009

This chapter discusses the energy critical nonlinear wave equation in 3 space dimensions. It mainly focuses on soliton resolution for radial solutions of nonlinear waves. For a long time there has been a widespread belief that global in time solutions of dispersive equations, asymptotically in time, decouple into a sum of finitely many modulated solitons, a free radiation term, and a term that goes to 0 at infinity. Such a result should hold for globally well-posed equations, or in general, with the additional condition that the solution does not blow-up. When blow-up may occur such decompositions are always expected to be unstable.

Keywords:   energy critical wave equation, energy critical nonlinear wave equation, 3D, soliton resolution, solitons

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