Schrödinger maps
Nai‐Heng Chang, Jalal Shatah, Karen Uhlenbeck · Communications on Pure and Applied Mathematics · 2000
We study the well-posedness of the Cauchy problem for Schrödinger maps from ℝm × ℝ into a compact Riemann surface N. The idea is to find an appropriate frame for u−1TN 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 𝕊1 symmetry on N. © 2000 John Wiley & Sons, Inc.