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A controlling norm for energy-critical Schrödinger maps


Authors: Benjamin Dodson and Paul Smith
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
Published electronically: April 2, 2015
MathSciNet review: 3378828
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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.


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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
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

DOI: https://doi.org/10.1090/S0002-9947-2015-06417-4
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.
Article copyright: © Copyright 2015 American Mathematical Society