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2012 Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation
Matthieu Hillairet, Pierre Raphaël
Anal. PDE 5(4): 777-829 (2012). DOI: 10.2140/apde.2012.5.777

Abstract

We exhibit C type II blow-up solutions to the focusing energy-critical wave equation in dimension N=4. These solutions admit near blow-up time a decomposition

u ( t , x ) = 1 λ ( N 2 ) 2 ( t ) ( Q + ε ( t ) ) ( x λ ( t ) ) , w i t h ε ( t ) , t ε ( t ) 1 × L 2 1 ,

where Q is the extremizing profile of the Sobolev embedding 1L2, and a blow-up speed

λ ( t ) = ( T t ) e | log ( T t ) | ( 1 + o ( 1 ) )  as  t T .

Citation

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Matthieu Hillairet. Pierre Raphaël. "Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation." Anal. PDE 5 (4) 777 - 829, 2012. https://doi.org/10.2140/apde.2012.5.777

Information

Received: 8 October 2010; Accepted: 13 May 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1329.35207
MathSciNet: MR3006642
Digital Object Identifier: 10.2140/apde.2012.5.777

Subjects:
Primary: 35Q51

Keywords: Blow-up, wave equation

Rights: Copyright © 2012 Mathematical Sciences Publishers

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