Global well-posedness for periodic generalized KdV equation

Jiguang Bao; Yifei Wu

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arXiv · 1308.4835

Global well-posedness for periodic generalized KdV equation

Jiguang Bao·Yifei Wu

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Abstract

In this paper, we show the global well-posedness for periodic gKdV equations in the space $H^s(\mathbb{T})$, $s\ge \frac12$ for quartic case, and $s> \frac59$ for quintic case. These improve the previous results of I-team in 2004. In particular, the result is sharp for quintic case. The main approaches are the I-method combining with the resonance decomposition developed by Miao et al in 2010, and a bilinear Strichartz estimate in periodic setting.

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Jiguang Bao, Yifei Wu. 2013-08-22. Global well-posedness for periodic generalized KdV equation. https://arxiv.org/abs/1308.4835

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