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arXiv · 0908.0782

The low regularity global solutions for the critical generalized KdV equation

Changxing Miao·Shuanglin Shao·Yifei Wu·Guixiang Xu
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Abstract

We prove that the Cauchy problem of the mass-critical generalized KdV equation is globally well-posed in Sobolev spaces $H^s(\R)$ for $s>6/13$. Of course, we require that the mass is strictly less than that of the ground state in the focusing case. The main approach is the "I-method" together with the multilinear correction analysis. Moreover, we use some "partially refined" argument to lower the upper control of the multiplier in the resonant interactions. The result improves the previous works of Fonseca, Linares, Ponce (2003) and Farah (2009).

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Changxing Miao, Shuanglin Shao, Yifei Wu, Guixiang Xu. 2009-08-06. The low regularity global solutions for the critical generalized KdV equation. https://doi.org/10.4310/dpde.2010.v7.n3.a4

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