A note on bilinear estimates and regularity of flow maps for nonlinear dispersive equations
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- Proc. Amer. Math. Soc. 136 (2008), 2881-2886 Request permission
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.References
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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
- MR Author ID: 785145
- Email: herr@math.berkeley.edu
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2881-2886
- MSC (2000): Primary 35Q53; Secondary 76B15, 35B30
- DOI: https://doi.org/10.1090/S0002-9939-08-09238-1
- MathSciNet review: 2399054