- Title Pages
- Dedication
- Contents
- Preface
- Chapter One Selected Theorems by Eli Stein
- Chapter Two Eli’s Impact: A Case Study
- Chapter Three On Oscillatory Integral Operators in Higher Dimensions
- Chapter Four Hölder Regularity for Generalized Master Equations with Rough Kernels
- Chapter Five Extremizers of a Radon Transform Inequality
- Chapter Six Should We Solve Plateau’s Problem Again?
- Chapter Seven Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms
- Chapter Eight Internal DLA for Cylinders
- Chapter Nine The Energy Critical Wave Equation in 3D
- Chapter Ten On the Bounded L2 Curvature Conjecture
- Chapter Eleven On Div-Curl for Higher Order
- Chapter Twelve Square Functions and Maximal Operators Associated with Radial Fourier Multipliers
- Chapter Thirteen Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in <sup>R</sup>3, and Newton Polyhedra <i>Detlef Müller</i>
- Chapter Fourteen Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length
- Chapter Fifteen Diagonal Estimates for Bergman Kernels in Monomial-Type Domains
- Chapter Sixteen On the Singularities of the Pluricomplex Green’s Function
- Chapter Seventeen Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs
- Chapter Eighteen On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature
- List of Contributors
- Index
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
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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- Title Pages
- Dedication
- Contents
- Preface
- Chapter One Selected Theorems by Eli Stein
- Chapter Two Eli’s Impact: A Case Study
- Chapter Three On Oscillatory Integral Operators in Higher Dimensions
- Chapter Four Hölder Regularity for Generalized Master Equations with Rough Kernels
- Chapter Five Extremizers of a Radon Transform Inequality
- Chapter Six Should We Solve Plateau’s Problem Again?
- Chapter Seven Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms
- Chapter Eight Internal DLA for Cylinders
- Chapter Nine The Energy Critical Wave Equation in 3D
- Chapter Ten On the Bounded L2 Curvature Conjecture
- Chapter Eleven On Div-Curl for Higher Order
- Chapter Twelve Square Functions and Maximal Operators Associated with Radial Fourier Multipliers
- Chapter Thirteen Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in <sup>R</sup>3, and Newton Polyhedra <i>Detlef Müller</i>
- Chapter Fourteen Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length
- Chapter Fifteen Diagonal Estimates for Bergman Kernels in Monomial-Type Domains
- Chapter Sixteen On the Singularities of the Pluricomplex Green’s Function
- Chapter Seventeen Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs
- Chapter Eighteen On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature
- List of Contributors
- Index