Schrodinger Flow Near Harmonic Maps

Details Schrodinger Flow Near Harmonic Maps Schrodinger Flow Near Harmonic Maps

2005-04-25

arxiv.org/abs/math/0504497v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

For the Schr\"odinger flow from $R^2 \times R^+$ to the 2-sphere $S^2$, it is not known if finite energy solutions can blow up in finite time. We study equivariant solutions whose energy is near the energy of the family of equivariant harmonic maps. We prove that such solutions remain close to the harmonic maps until the blow up time (if any), and that they blow up if and only if the length scale of the nearest harmonic map goes to zero.

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