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

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- by Frank Merle
- J. Amer. Math. Soc.
**14**(2001), 555-578 - DOI: https://doi.org/10.1090/S0894-0347-01-00369-1
- Published electronically: March 20, 2001
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## 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.## References

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## Bibliographic 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: https://doi.org/10.1090/S0894-0347-01-00369-1
- MathSciNet review: 1824989