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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Blow up in finite time and dynamics of blow up solutions for the $L^2$-critical generalized KdV equation


Authors: Yvan Martel and Frank Merle
Journal: J. Amer. Math. Soc. 15 (2002), 617-664
MSC (1991): Primary 35Q53; Secondary 35B05, 35Q51
Published electronically: March 8, 2002
MathSciNet review: 1896235
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Abstract: In this paper, we describe the dynamics of blow up solutions for the critical generalized KdV equation such that the initial data is close to the soliton in $L^2$ and has decay in $L^2$ at the right. In particular, we prove that blow up occurs in finite time, and we obtain an upper bound on the blow up rate.


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Additional Information

Yvan Martel
Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, av. A. Chauvin, 95302 Cergy Pontoise, France
Email: Yvan.Martel@math.u-cergy.fr

Frank Merle
Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, av. A. Chauvin, 95302 Cergy Pontoise, France – and – Institut Universitaire de France
Email: Frank.Merle@math.u-cergy.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-02-00392-2
PII: S 0894-0347(02)00392-2
Keywords: Critical KdV equation, finite time blow up, blow up rate
Received by editor(s): March 15, 2001
Published electronically: March 8, 2002
Article copyright: © Copyright 2002 American Mathematical Society