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

Lan, Yang

Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 19, 9 p.

In this paper we consider the slightly $L^2$-supercritical gKdV equations ${\partial }_{t}u+(u_{xx}+{u\left|u\right|}^{p-1}{)}_x=0$, with the nonlinearity $5<p<5+\epsilon$ and $0<\epsilon \ll 1$ . We will prove the existence and stability of a blow-up dynamics with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.

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