## A controlling norm for energy-critical Schrödinger maps

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- by Benjamin Dodson and Paul Smith PDF
- Trans. Amer. Math. Soc.
**367**(2015), 7193-7220 Request permission

## Abstract:

We consider energy-critical Schrödinger maps with target either the sphere $\mathbb {S}^2$ or hyperbolic plane $\mathbb {H}^2$ and establish that a unique solution may be continued so long as a certain space-time $L^4$ norm remains bounded. This reduces the large data global wellposedness problem to that of controlling this norm.## References

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## Additional Information

**Benjamin Dodson**- Affiliation: Department of Mathematics, 970 Evans Hall, University of California, Berkeley, California 94720-3840
- Address at time of publication: Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, Baltimore, Maryland 21218
- MR Author ID: 891326
- Email: benjadod@math.berkeley.edu, dodson@math.jhu.edu
**Paul Smith**- Affiliation: Department of Mathematics, 970 Evans Hall, University of California, Berkeley, California 94720-3840
- Address at time of publication: Google, 1600 Amphitheatre Parkway, Mountain View, California 94043
- Email: smith@math.berkeley.edu
- Received by editor(s): February 18, 2013
- Received by editor(s) in revised form: August 15, 2013
- Published electronically: April 2, 2015
- Additional Notes: The first author was supported by NSF grant DMS-1103914 and the second by NSF grant DMS-1103877.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**367**(2015), 7193-7220 - MSC (2010): Primary 35Q55; Secondary 35B33
- DOI: https://doi.org/10.1090/S0002-9947-2015-06417-4
- MathSciNet review: 3378828