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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Bibliographic Details
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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Summary: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.
ISSN:2524-5317
2199-2576
DOI:10.1007/s40818-023-00159-4