### Abstract

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 script S sign^{1} symmetry on N.

Original language | English (US) |
---|---|

Pages (from-to) | 590-602 |

Number of pages | 13 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 53 |

Issue number | 5 |

State | Published - May 2000 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*53*(5), 590-602.

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 53, no. 5, pp. 590-602.

}

TY - JOUR

T1 - Schrödinger maps

AU - Chang, Nai Heng

AU - Shatah, Jalal

AU - Uhlenbeck, Karen

PY - 2000/5

Y1 - 2000/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034415649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034415649&partnerID=8YFLogxK

M3 - Article

VL - 53

SP - 590

EP - 602

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 5

ER -