Global Schrödinger maps

Bejenaru, Ioan; Ionescu, Alexandru D.; Kenig, Carlos E.; Tataru, Daniel

Global Schrödinger maps

Authors

Bejenaru, Ioan

Ionescu, Alexandru D.

Kenig, Carlos E.

Tataru, Daniel

Description

We consider the Schrödinger map initial-value problem in dimension two or greater. We prove that the Schrödinger 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.
60 pages