Global existence and uniqueness of Schrodinger maps in dimensions d >= 4

摘要

In dimensions d >= 4, we prove that the Schrodinger map initial-value problem [GRAPHICS] admits a unique solution s: R-d x R -> S-2 -> R-3, s is an element of C(R : H-Q(infinity)), provided that s(0) is an element of H-Q(infinity) and parallel to s(0) - Q parallel to H-d/2 1, where Q is an element of S-2. (c) 2007 Elsevier Inc. All rights reserved.