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Global well-posedness for KdV in Sobolev spaces of negative index

Colliander, James and Keel, Markus and Staffilani, Gigliola and Takaoka, Hideo and Tao, Terence (2001) Global well-posedness for KdV in Sobolev spaces of negative index. Electronic Journal of Differential Equations, 2001 (26). pp. 1-7. ISSN 1072-6691. http://resolver.caltech.edu/CaltechAUTHORS:COLejde01

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Abstract

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in $H^s(\mathbb{R})$ for -3/10 < s.


Item Type:Article
Additional Information:© 2001 Southwest Texas State University. Submitted January 31, 2001. Published April 27, 2001. J.E.C. is supported in part by an N.S.F. Postdoctoral Research Fellowship. M.K. is supported in part by N.S.F. Grant DMS 9801558. G.S. is supported in part by N.S.F. Grant DMS 9800879 and by a Terman Award. T.T. is a Clay Prize Fellow and is supported in part by grants from the Packard and Sloan Foundations.
Subject Keywords:Korteweg-de Vries equation, nonlinear dispersive equations, bilinear estimates
Record Number:CaltechAUTHORS:COLejde01
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:COLejde01
Alternative URL:http://www.emis.ams.org/journals/EJDE/Volumes/2001/26/abstr.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1228
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:05 Jan 2006
Last Modified:26 Dec 2012 08:43

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