Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions D ≥ 4 . This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W , called the ground state. We prove that every finite energy solution wit...

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Published in:Annals of PDE 2023-12, Vol.9 (2), p.18, Article 18
Main Authors: Jendrej, Jacek, Lawrie, Andrew
Format: Article
Language:English
Subjects:
Analysis of PDEs
Bubbles
Cauchy problems
Energy
Ground state
Mathematical Methods in Physics
Mathematics
Partial Differential Equations
Physics
Physics and Astronomy
Radiation
Solitary waves
Wave equations
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description We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions D ≥ 4 . This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W , called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.
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subjects Analysis of PDEs
Bubbles
Cauchy problems
Energy
Ground state
Mathematical Methods in Physics
Mathematics
Partial Differential Equations
Physics
Physics and Astronomy
Radiation
Solitary waves
Wave equations
title Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case
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