| Résume | Expanding self-similarities of a given evolution equation create an ambiguity in the continuation of the flow after it reached a first singularity. In this talk, we investigate the possibility of smoothing out any map from the n-sphere, n>1, to another sphere, that is homotopic to a constant by a self-similarity of the harmonic map flow. To do so, in the spirit of Chen-Struwe, we introduce a one-parameter family of Ginzburg-Landau equations that exhibit the same homogeneity and once the existence of expanders for this family is granted, we pass to the limit. We also study the singular set of such solutions as well as the uniqueness issue. |
