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

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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 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.

Original language	English
Pages (from-to)	317-355
Number of pages	39
Journal	Journal des Mathematiques Pures et Appliquees
Volume	139
DOIs	https://doi.org/10.1016/j.matpur.2020.02.007
Publication status	Published - 1 Jul 2020
Externally published	Yes

Keywords

Energy-critical
Ground state
Multi-bubble
Wave equation

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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.",

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author = "Jacek Jendrej and Yvan Martel",

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year = "2020",

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AU - Jendrej, Jacek

AU - Martel, Yvan

PY - 2020/7/1

Y1 - 2020/7/1

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

AN - SCOPUS:85079843543

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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Keywords

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