Year: 2005
Type: preprint
Abstract: For the Schrödinger 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.
Source: arXiv (Cornell University)
Authors: Gustafson, S., Kang, K., Tsai, T. -P.
Institutions: University of British Columbia, Sungkyunkwan University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953020012