Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5

Jacek Jendrej; Yvan Martel

doi:10.1016/j.matpur.2020.02.007

Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5

Jacek Jendrej
, Yvan Martel

University Paris 13
Centre de Mathématiques Laurent Schwartz Ecole Polytechnique

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

Résumé

We prove the existence of a global solution of the energy-critical focusing wave equation in dimension 5 blowing up in infinite time at any K given points z_k of R⁵, where K≥2. The concentration rate of each bubble is asymptotic to c_kt⁻² as t→∞, where the c_k are positive constants depending on the distances between the blow-up points z_k. This result complements previous constructions of blow-up solutions and multi-solitons of the energy-critical wave equation in various dimensions N≥3.

langue originale	Anglais
Pages (de - à)	317-355
Nombre de pages	39
journal	Journal des Mathematiques Pures et Appliquees
Volume	139
Les DOIs	https://doi.org/10.1016/j.matpur.2020.02.007
état	Publié - 1 juil. 2020
Modification externe	Oui

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10.1016/j.matpur.2020.02.007

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title = "Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5",

abstract = "We prove the existence of a global solution of the energy-critical focusing wave equation in dimension 5 blowing up in infinite time at any K given points zk of R5, where K≥2. The concentration rate of each bubble is asymptotic to ckt−2 as t→∞, where the ck are positive constants depending on the distances between the blow-up points zk. This result complements previous constructions of blow-up solutions and multi-solitons of the energy-critical wave equation in various dimensions N≥3.",

keywords = "Energy-critical, Ground state, Multi-bubble, Wave equation",

author = "Jacek Jendrej and Yvan Martel",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Masson SAS",

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doi = "10.1016/j.matpur.2020.02.007",

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AU - Jendrej, Jacek

AU - Martel, Yvan

PY - 2020/7/1

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N2 - We prove the existence of a global solution of the energy-critical focusing wave equation in dimension 5 blowing up in infinite time at any K given points zk of R5, where K≥2. The concentration rate of each bubble is asymptotic to ckt−2 as t→∞, where the ck are positive constants depending on the distances between the blow-up points zk. This result complements previous constructions of blow-up solutions and multi-solitons of the energy-critical wave equation in various dimensions N≥3.

AB - We prove the existence of a global solution of the energy-critical focusing wave equation in dimension 5 blowing up in infinite time at any K given points zk of R5, where K≥2. The concentration rate of each bubble is asymptotic to ckt−2 as t→∞, where the ck are positive constants depending on the distances between the blow-up points zk. This result complements previous constructions of blow-up solutions and multi-solitons of the energy-critical wave equation in various dimensions N≥3.

KW - Energy-critical

KW - Ground state

KW - Multi-bubble

KW - Wave equation

U2 - 10.1016/j.matpur.2020.02.007

DO - 10.1016/j.matpur.2020.02.007

M3 - Article

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SN - 0021-7824

VL - 139

SP - 317

EP - 355

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5

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