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Schrödinger maps

✍ Scribed by Nai-Heng Chang; Jalal Shatah; Karen Uhlenbeck

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
74 KB
Volume
53
Category
Article
ISSN
0010-3640

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✦ Synopsis

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 T N 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 S 1 symmetry on N.

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