Vol. 5, No. 4, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation

Matthieu Hillairet and Pierre Raphaël

Vol. 5 (2012), No. 4, 777–829
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(N2)2(t)(Q + ε(t))( x λ(t)),with ε(t),tε(t)1×L2 1,

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

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

Keywords
wave equation, blow-up
Mathematical Subject Classification 2010
Primary: 35Q51
Milestones
Received: 8 October 2010
Accepted: 13 May 2011
Published: 27 November 2012
Authors
Matthieu Hillairet
Ceremade
Université Paris Dauphine
75775 Paris Cedex 16
France
http://www.ceremade.dauphine.fr/~mhillair/
Pierre Raphaël
Université Paul Sabatier
Institut de Mathématiques de Toulouse
31062 Toulouse Cedex 9
France
http://www.math.univ-toulouse.fr/~raphael/