Stable self-similar blow-up dynamics for slightly L 2 -supercritical generalized KDV equations
Yang Lan1
1 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Université Paris-Saclay 91405 Orsay France
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 ∂ t u+(u xx +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 H 1 and give a specific description of the formation of the singularity near the blow-up time.

Publié le :
DOI : 10.5802/slsedp.93
Yang Lan 1

1 Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Université Paris-Saclay 91405 Orsay France 
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Yang Lan. Stable self-similar blow-up dynamics for slightly $L^2$-supercritical generalized KDV equations. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 19, 9 p. doi : 10.5802/slsedp.93. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.93/

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