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Zbl 1028.35134
Chang, Nai-Heng; Shatah, Jalal; Uhlenbeck, Karen
Schrödinger maps. (English)
[J] Commun. Pure Appl. Math. 53, No.5, 590-602 (2000). ISSN 0010-3640

The authors consider the Cauchy problem for Schrödinger maps into a compact Riemann surface. In one space dimension, for finite energy data, it is shown that the problem has a global unique solution, and that for smooth initial data the solution is smooth. In two space dimensions, for radial or equivariant maps, small energy is shown to imply global existence and uniqueness and further, for smooth initial data, regularity.
[A.Pickering (Salamanca)]

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
53C44 Geometric evolution equations (mean curvature flow)
58J90 Applications

Keywords: nonlinear Schrödinger equation; Schrödinger maps; Cauchy problem; compact Riemann surface; global existence; regularity; finite energy data; global uniqueness

Cited in: Zbl 1013.58007

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