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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Global well-posedness of the Benjamin-Ono equation in low-regularity spaces


Authors: Alexandru D. Ionescu and Carlos E. Kenig
Journal: J. Amer. Math. Soc. 20 (2007), 753-798
MSC (2000): Primary 35Q53
DOI: https://doi.org/10.1090/S0894-0347-06-00551-0
Published electronically: October 24, 2006
MathSciNet review: 2291918
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Abstract: We prove that the Benjamin-Ono initial-value problem is globally well-posed in the Banach spaces $ H^\sigma_r(\mathbb{R})$, $ \sigma\geq 0$, of real-valued Sobolev functions.


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Additional Information

Alexandru D. Ionescu
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Van Vleck Hall, Madison, Wisconsin 53706
Email: ionescu@math.wisc.edu

Carlos E. Kenig
Affiliation: Department of Mathematics, University of Chicago, 5734 University Ave, Chicago, Illinois 60637-1514
Email: cek@math.uchicago.edu

DOI: https://doi.org/10.1090/S0894-0347-06-00551-0
Keywords: Benjamin--Ono initial-value problem, global well-posedness, local smoothing, gauge transformation
Received by editor(s): October 10, 2005
Published electronically: October 24, 2006
Additional Notes: The first author was supported in part by an NSF grant, a Sloan Research Fellowship, and a Packard Fellowship.
The second author was supported in part by an NSF grant.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.