Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems

Pierre Raphaël[1]; Igor Rodnianski[2]

  • [1] Institut de Mathématiques de Toulouse Université Toulouse III France
  • [2] Mathematics Department Princeton University USA

Séminaire Équations aux dérivées partielles (2008-2009)

  • Volume: 115, page 1-12

Abstract

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This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the 𝕊 2 target in all homotopy classes and for the equivariant critical S O ( 4 ) Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.

How to cite

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Raphaël, Pierre, and Rodnianski, Igor. "Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems." Séminaire Équations aux dérivées partielles 115 (2008-2009): 1-12. <http://eudml.org/doc/11195>.

@article{Raphaël2008-2009,
abstract = {This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the $\{\mathbb\{S\}\}^2$ target in all homotopy classes and for the equivariant critical $SO(4)$ Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.},
affiliation = {Institut de Mathématiques de Toulouse Université Toulouse III France; Mathematics Department Princeton University USA},
author = {Raphaël, Pierre, Rodnianski, Igor},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {wave map problem; Yang-Mills problem; initial data; blow-up; self-similar solution; boot-strap argument},
language = {eng},
pages = {1-12},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems},
url = {http://eudml.org/doc/11195},
volume = {115},
year = {2008-2009},
}

TY - JOUR
AU - Raphaël, Pierre
AU - Rodnianski, Igor
TI - Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems
JO - Séminaire Équations aux dérivées partielles
PY - 2008-2009
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 115
SP - 1
EP - 12
AB - This note summarizes the results obtained in [30]. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the ${\mathbb{S}}^2$ target in all homotopy classes and for the equivariant critical $SO(4)$ Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.
LA - eng
KW - wave map problem; Yang-Mills problem; initial data; blow-up; self-similar solution; boot-strap argument
UR - http://eudml.org/doc/11195
ER -

References

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