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

Merle, Frank

doi:10.1090/S0894-0347-01-00369-1

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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
Posted: March 20, 2001
MathSciNet review: 1824989
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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.

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