TY - JOUR
T1 - Self-similar solutions for the Schrödinger map equation
AU - Germain, Pierre
AU - Shatah, Jalal
AU - Zeng, Chongchun
PY - 2010/1
Y1 - 2010/1
N2 - We study in this article the equivariant Schrödinger map equation in dimension 2, from the Euclidean plane to the sphere. A family of self-similar solutions is constructed; this provides an example of regularity breakdown for the Schrödinger map. These solutions do not have finite energy, and hence do not fit into the usual framework for solutions. For data of infinite energy but small in some norm, we build up associated global solutions.
AB - We study in this article the equivariant Schrödinger map equation in dimension 2, from the Euclidean plane to the sphere. A family of self-similar solutions is constructed; this provides an example of regularity breakdown for the Schrödinger map. These solutions do not have finite energy, and hence do not fit into the usual framework for solutions. For data of infinite energy but small in some norm, we build up associated global solutions.
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U2 - 10.1007/s00209-009-0492-0
DO - 10.1007/s00209-009-0492-0
M3 - Article
AN - SCOPUS:76349116071
SN - 0025-5874
VL - 264
SP - 697
EP - 707
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -