Elsevier

Advances in Mathematics

Volume 215, Issue 1, 20 October 2007, Pages 263-291
Advances in Mathematics

Global existence and uniqueness of Schrödinger maps in dimensions d4

https://doi.org/10.1016/j.aim.2007.04.009Get rights and content
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Abstract

In dimensions d4, we prove that the Schrödinger map initial-value problem{ts=s×ΔsonRd×R;s(0)=s0 admits a unique solution s:Rd×RS2R3, sC(R:HQ), provided that s0HQ and s0QH˙d/21, where QS2.

Keywords

Schrödinger maps
Modified Schrödinger maps
Orthonormal frames
A priori estimates

Cited by (0)

The second author was supported in part by an NSF grant and a Packard fellowship. The third author was supported in part by an NSF grant.