# Schrödinger maps

Nai Heng Chang, Jalal Shatah, Karen Uhlenbeck

Research output: Contribution to journalArticle

### Abstract

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 script S sign1 symmetry on N.

Original language English (US) 590-602 13 Communications on Pure and Applied Mathematics 53 5 Published - May 2000

### Fingerprint

Nonlinear equations
Derivatives
Strichartz Estimates
A Priori Estimates
Energy
Riemann Surface
Well-posedness
Cauchy Problem
Nonlinear Equations
Symmetry
Derivative
Class

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

Chang, N. H., Shatah, J., & Uhlenbeck, K. (2000). Schrödinger maps. Communications on Pure and Applied Mathematics, 53(5), 590-602.

Schrödinger maps. / Chang, Nai Heng; Shatah, Jalal; Uhlenbeck, Karen.

In: Communications on Pure and Applied Mathematics, Vol. 53, No. 5, 05.2000, p. 590-602.

Research output: Contribution to journalArticle

Chang, NH, Shatah, J & Uhlenbeck, K 2000, 'Schrödinger maps', Communications on Pure and Applied Mathematics, vol. 53, no. 5, pp. 590-602.
Chang NH, Shatah J, Uhlenbeck K. Schrödinger maps. Communications on Pure and Applied Mathematics. 2000 May;53(5):590-602.
Chang, Nai Heng ; Shatah, Jalal ; Uhlenbeck, Karen. / Schrödinger maps. In: Communications on Pure and Applied Mathematics. 2000 ; Vol. 53, No. 5. pp. 590-602.
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