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

Jacek Jendrej; Andrew Lawrie

doi:10.1007/s40818-023-00159-4

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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	18
Journal	Annals of PDE
Volume	9
Issue number	2
DOIs	https://doi.org/10.1007/s40818-023-00159-4
Publication status	Published - 1 Dec 2023
Externally published	Yes

Keywords

Energy-critical
Multi-soliton
Soliton resolution
Wave maps

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10.1007/s40818-023-00159-4

Cite this

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title = "Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case",

abstract = "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.",

keywords = "Energy-critical, Multi-soliton, Soliton resolution, Wave maps",

author = "Jacek Jendrej and Andrew Lawrie",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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T1 - Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case

AU - Jendrej, Jacek

AU - Lawrie, Andrew

PY - 2023/12/1

Y1 - 2023/12/1

N2 - 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.

AB - 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.

KW - Energy-critical

KW - Multi-soliton

KW - Soliton resolution

KW - Wave maps

U2 - 10.1007/s40818-023-00159-4

DO - 10.1007/s40818-023-00159-4

M3 - Article

AN - SCOPUS:85173967345

SN - 2524-5317

VL - 9

JO - Annals of PDE

JF - Annals of PDE

IS - 2

M1 - 18

ER -

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

Abstract

Keywords

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