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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on bilinear estimates and regularity of flow maps for nonlinear dispersive equations


Author: Sebastian Herr
Journal: Proc. Amer. Math. Soc. 136 (2008), 2881-2886
MSC (2000): Primary 35Q53; Secondary 76B15, 35B30
Published electronically: April 8, 2008
MathSciNet review: 2399054
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Abstract: Explicit counterexamples to bilinear estimates related to the Benjamin-Ono equation in the periodic setting are calculated for functions of zero mean value. As a consequence, certain bilinear estimates fail to hold in spite of the analyticity of the flow map. The latter has been shown recently by L. Molinet.


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Additional Information

Sebastian Herr
Affiliation: Technische Universität Dortmund, Fakultät für Mathematik, 44221 Dortmund, Germany
Address at time of publication: Center for Pure and Applied Mathematics, University of California, 837 Evans Hall, Berkeley, California 94720-3840
Email: herr@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09238-1
PII: S 0002-9939(08)09238-1
Keywords: Failure of bilinear estimates, periodic Benjamin-Ono equation
Received by editor(s): April 17, 2007
Published electronically: April 8, 2008
Additional Notes: The author is grateful to M. Hadac, H. Koch, and N. Tzvetkov for valuable discussions on the subject. This research is part of the author’s doctoral dissertation, which has been awarded a Dissertationspreis at Dortmund University
Communicated by: Hart F. Smith
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.