Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

Pierre Raphaël; Igor Rodnianski

doi:10.1007/s10240-011-0037-z

Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

Pierre Raphaël
, Igor Rodnianski

Mathematics

Research output: Contribution to journal › Article › peer-review

145 Scopus citations

Abstract

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 critical equivariant 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.

Original language	English (US)
Pages (from-to)	1-122
Number of pages	122
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	115
Issue number	1
DOIs	https://doi.org/10.1007/s10240-011-0037-z
State	Published - Jun 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s10240-011-0037-z

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title = "Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems",

abstract = "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 critical equivariant 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.",

author = "Pierre Rapha{\"e}l and Igor Rodnianski",

note = "Funding Information: Both authors would like to thank the anonymous referee for his careful reading of the paper and his very many suggestions to improve the paper. This work was partly done while P.R. was visiting Princeton University and I.R. the Institut de Mathematiques de Toulouse, and both authors would like to thank these institutions for their hospitality. The authors also wish to acknowledge discussions with J. Sterbenz concerning early stages of this work. P.R. is supported by the ANR Jeunes Chercheurs SWAP. I.R. is supported by the NSF grant DMS-0702270.",

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AU - Rodnianski, Igor

N1 - Funding Information: Both authors would like to thank the anonymous referee for his careful reading of the paper and his very many suggestions to improve the paper. This work was partly done while P.R. was visiting Princeton University and I.R. the Institut de Mathematiques de Toulouse, and both authors would like to thank these institutions for their hospitality. The authors also wish to acknowledge discussions with J. Sterbenz concerning early stages of this work. P.R. is supported by the ANR Jeunes Chercheurs SWAP. I.R. is supported by the NSF grant DMS-0702270.

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AB - 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 critical equivariant 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.

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Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

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