Schrodinger Flow Near Harmonic Maps

Research paper by S. Gustafson, K. Kang, T. -P. Tsai

Indexed on: 25 Apr '05Published on: 25 Apr '05Published in: Mathematics - Analysis of PDEs


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.