Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case

Thomas Duyckaerts; Carlos E. Kenig; Frank Merle

Journal of the European Mathematical Society (2012)

  • Volume: 014, Issue: 5, page 1389-1454
  • ISSN: 1435-9855

Abstract

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Following our previous paper in the radial case, we consider type II blow-up solutions to the energy-critical focusing wave equation. Let W be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under an appropriate smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of W concentrating at the origin.

How to cite

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Duyckaerts, Thomas, Kenig, Carlos E., and Merle, Frank. "Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case." Journal of the European Mathematical Society 014.5 (2012): 1389-1454. <http://eudml.org/doc/277276>.

@article{Duyckaerts2012,
abstract = {Following our previous paper in the radial case, we consider type II blow-up solutions to the energy-critical focusing wave equation. Let W be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under an appropriate smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of $W$ concentrating at the origin.},
author = {Duyckaerts, Thomas, Kenig, Carlos E., Merle, Frank},
journal = {Journal of the European Mathematical Society},
keywords = {rescaled Lorentz transform},
language = {eng},
number = {5},
pages = {1389-1454},
publisher = {European Mathematical Society Publishing House},
title = {Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case},
url = {http://eudml.org/doc/277276},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Duyckaerts, Thomas
AU - Kenig, Carlos E.
AU - Merle, Frank
TI - Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 5
SP - 1389
EP - 1454
AB - Following our previous paper in the radial case, we consider type II blow-up solutions to the energy-critical focusing wave equation. Let W be the unique radial positive stationary solution of the equation. Up to the symmetries of the equation, under an appropriate smallness assumption, any type II blow-up solution is asymptotically a regular solution plus a rescaled Lorentz transform of $W$ concentrating at the origin.
LA - eng
KW - rescaled Lorentz transform
UR - http://eudml.org/doc/277276
ER -

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