Schrödinger maps. (English) Zbl 1028.35134

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.


35Q55 NLS equations (nonlinear Schrödinger equations)
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
58J90 Applications of PDEs on manifolds
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