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arXiv · 0910.1389

On the regularization mechanism for the periodic Korteweg-de Vries equation

Anatoli V. Babin·Alexei A. Ilyin·Edriss S. Titi
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Abstract

In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg--de Vries (KdV) equation in the homogeneous Sobolev spaces $\dot{H}^s$, for $s\ge0$. Specifically, we prove the global existence, uniqueness, and Lipschitz continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in $L_2$ we also show the Lipschitz continuous dependence of these solutions with respect to the initial data as maps from $\dot{H}^s$ to $\dot{H}^s$, for $s\in(-1,0]$.

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Anatoli V. Babin, Alexei A. Ilyin, Edriss S. Titi. 2010-10-23. On the regularization mechanism for the periodic Korteweg-de Vries equation. https://arxiv.org/abs/0910.1389

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