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Journal of the American Mathematical Society

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Existence of blow-up solutions in the energy space for the critical generalized KdV equation
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by Frank Merle PDF
J. Amer. Math. Soc. 14 (2001), 555-578 Request permission


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
  • MR Author ID: 123710
  • Received by editor(s): July 25, 2000
  • Received by editor(s) in revised form: November 1, 2000
  • Published electronically: March 20, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 555-578
  • MSC (2000): Primary 35B35, 35Q53
  • DOI:
  • MathSciNet review: 1824989