Nonexistence of two-bubbles with opposite signs for the radial energy-critical wave equation

Jacek Jendrej

doi:10.2422/2036-2145.201511_001

Nonexistence of two-bubbles with opposite signs for the radial energy-critical wave equation

Jacek Jendrej

Institut Galilée

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

10 Citations (Scopus)

Résumé

We consider the focusing energy-critical wave equation in space dimension N ! 3 for radial data. We study two-bubble solutions, that is solutions which behave as a superposition of two decoupled radial ground states (called bubbles) asymptotically for large positive times. We prove that in this case these two bubbles must have the same sign. The main tool is a sharp coercivity property of the energy functional near the family of ground states.

langue originale	Anglais
Pages (de - à)	735-778
Nombre de pages	44
journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	18
Numéro de publication	2
Les DOIs	https://doi.org/10.2422/2036-2145.201511_001
état	Publié - 1 janv. 2018
Modification externe	Oui

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10.2422/2036-2145.201511_001

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abstract = "We consider the focusing energy-critical wave equation in space dimension N ! 3 for radial data. We study two-bubble solutions, that is solutions which behave as a superposition of two decoupled radial ground states (called bubbles) asymptotically for large positive times. We prove that in this case these two bubbles must have the same sign. The main tool is a sharp coercivity property of the energy functional near the family of ground states.",

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AB - We consider the focusing energy-critical wave equation in space dimension N ! 3 for radial data. We study two-bubble solutions, that is solutions which behave as a superposition of two decoupled radial ground states (called bubbles) asymptotically for large positive times. We prove that in this case these two bubbles must have the same sign. The main tool is a sharp coercivity property of the energy functional near the family of ground states.

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DO - 10.2422/2036-2145.201511_001

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Nonexistence of two-bubbles with opposite signs for the radial energy-critical wave equation

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