Global Schrödinger maps

Details Global Schrödinger maps Global Schrödinger maps

2008-07-02

arxiv.org/abs/0807.0265v1

Mathematics

Analysis of PDEs

60 pages

Scientific paper

We consider the Schr\"{o}dinger map initial-value problem in dimension two or
greater. We prove that the Schr\"{o}dinger map initial-value problem admits a
unique global smooth solution, provided that the initial data is smooth and
small in the critical Sobolev space. We prove also that the solution operator
extends continuously to the critical Sobolev space.

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