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In this paper we consider the slightly L2-supercritical gKdV equations ∂tu + (uxx + u|u|p−1)x = 0, with the nonlinearity 5 < p < 5 + ε and 0 < ε 1 . We will prove the existence and stability of a blow-up dynamics with self-similar blow-up rate in the energy space H1 and give a specific description of the formation of the singularity near the blow-up time.

séminaire laurent schwartz

Stable self-similar blow-up dynamics for slightly <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math>-supercritical generalized KDV equations

Stable self-similar blow-up dynamics for slightly L 2 -supercritical generalized KDV equations