On the Formation of Singularities in the Critical O(3) Σ-model

@inproceedings{RODNIANSKI2008OnTF,
  title={On the Formation of Singularities in the Critical O(3) Σ-model},
  author={IGOR RODNIANSKI and JACOB STERBENZ},
  year={2008}
}
  • IGOR RODNIANSKI, JACOB STERBENZ
  • Published 2008
We study the phenomena of energy concentration for the critical O(3) sigma model, also known as the wave map flow from R2+1 Minkowski space into the sphere S2. We establish rigorously and constructively existence of a set of smooth initial data resulting in a dynamic finite time formation of singularities. The construction and analysis is done in the context of the k-equivariant symmetry reduction, and we restrict to maps with homotopy class k > 4. The concentration mechanism we uncover is… CONTINUE READING
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