Geodesic
Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
Raphaël, Pierre1  ; Rodnianski, Igor2 
1 Institut de Mathématiques de Toulouse, Université Toulouse III 31062, Toulouse France
2 Mathematics Department, Princeton University Princeton, NJ, 08544 USA
Publications Mathématiques de l'IHÉS, Tome 115 (2012), pp. 1-122

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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.

DOI : 10.1007/s10240-011-0037-z

Raphaël, Pierre 1 ; Rodnianski, Igor 2

1 Institut de Mathématiques de Toulouse, Université Toulouse III 31062, Toulouse France
2 Mathematics Department, Princeton University Princeton, NJ, 08544 USA 
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     title = {Stable blow up dynamics for the critical co-rotational wave maps and equivariant {Yang-Mills} problems},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--122},
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Raphaël, Pierre; Rodnianski, Igor. Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems. Publications Mathématiques de l'IHÉS, Tome 115 (2012), pp. 1-122. doi: 10.1007/s10240-011-0037-z

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