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Existence of blow-up solutions in the energy space for the critical generalized KdV equation


Author: Frank Merle
Journal: J. Amer. Math. Soc. 14 (2001), 555-578
MSC (2000): Primary 35B35, 35Q53
Published electronically: March 20, 2001
MathSciNet review: 1824989
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Abstract | References | Similar Articles | Additional Information

Abstract:

For the critical generalized Korteweg-de Vries equation, we establish blow-up in finite or infinite time in $H^1(\mathbf R)$ for initial data with negative energy, close to a soliton up to scaling and translation.


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Additional Information

Frank Merle
Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, avenue Adolphe Chauvin, BP 222, 95302 Cergy–Pontoise, France

DOI: https://doi.org/10.1090/S0894-0347-01-00369-1
Keywords: Blow-up, critical, KdV
Received by editor(s): July 25, 2000
Received by editor(s) in revised form: November 1, 2000
Published electronically: March 20, 2001
Article copyright: © Copyright 2001 American Mathematical Society