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

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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.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Toulouse III, 31062, Toulouse, France

    Pierre Raphaël

  2. Mathematics Department, Princeton University, Princeton, NJ, 08544, USA

    Igor Rodnianski

Authors
  1. Pierre Raphaël
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  2. Igor Rodnianski
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Correspondence to Pierre Raphaël.

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Raphaël, P., Rodnianski, I. Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems. Publ.math.IHES 115, 1–122 (2012). https://doi.org/10.1007/s10240-011-0037-z

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  • DOI: https://doi.org/10.1007/s10240-011-0037-z

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