Schrödinger maps

Nai Heng Chang; Jalal Shatah; Karen Uhlenbeck

doi:10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R

Schrödinger maps

Nai Heng Chang, Jalal Shatah, Karen Uhlenbeck

Mathematics

Research output: Contribution to journal › Article › peer-review

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^-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)
Pages (from-to)	590-602
Number of pages	13
Journal	Communications on Pure and Applied Mathematics
Volume	53
Issue number	5
DOIs	https://doi.org/10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R
State	Published - May 2000

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R

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title = "Schr{\"o}dinger maps",

abstract = "We study the well-posedness of the Cauchy problem for Schr{\"o}dinger 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 Schr{\"o}dinger 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.",

author = "Chang, {Nai Heng} and Jalal Shatah and Karen Uhlenbeck",

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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.

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VL - 53

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EP - 602

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 5

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Schrödinger maps

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