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Schrödinger maps
Author(s) -
Chang NaiHeng,
Shatah Jalal,
Uhlenbeck Karen
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200005)53:5<590::aid-cpa2>3.0.co;2-r
Subject(s) - mathematics , schrödinger's cat , mathematical physics
We study the well‐posedness of the Cauchy problem for Schrödinger maps from ℝ m × ℝ into a compact Riemann surface N . The idea is to find an appropriate frame for u −1 TN so that the derivatives will satisfy a certain class of nonlinear Schrödinger equations; then the Strichartz estimates can be applied to obtain a priori estimates. We treat the problem with finite energy data for m = 1 and with small energy data for m = 2 under an assumption of radial or 1 symmetry on N . © 2000 John Wiley & Sons, Inc.