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Stable Self-Similar Blow-Up Dynamics for Slightly \({L^2}\)-Supercritical Generalized KDV Equations

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Abstract

In this paper we consider the slightly \({L^2}\)-supercritical gKdV equations \({\partial_t u+(u_{xx}+u|u|^{p-1})_x=0}\), with the nonlinearity \({5 < p < 5+\varepsilon}\) and \({0 < \varepsilon\ll 1}\). 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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  1. Laboratoire de Mathematiques D’Orsay, Universite Paris-Sud, Orsay, France

    Yang Lan

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  1. Yang Lan
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Correspondence to Yang Lan.

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Communicated by W. Schlag

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Lan, Y. Stable Self-Similar Blow-Up Dynamics for Slightly \({L^2}\)-Supercritical Generalized KDV Equations. Commun. Math. Phys. 345, 223–269 (2016). https://doi.org/10.1007/s00220-016-2589-8

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