Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map

Details Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map

2011-06-05

arxiv.org/abs/1106.0912v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the energy critical Schr\"odinger map problem with the 2-sphere target for equivariant initial data of homotopy index $k=1$. We show the existence of a codimension one set of smooth well localized initial data arbitrarily close to the ground state harmonic map in the energy critical norm, which generates finite time blow up solutions. We give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy.

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