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Mathematics  2009 

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 the blow up time and prove quantization of the energy focused at the singularity.

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