Mathematics – Analysis of PDEs
Scientific paper
2009-08-06
Dynamics of PDE, Vol.7, No.3, 265-288, 2010
Mathematics
Analysis of PDEs
27pages, the mistake in the previous version is corrected; using I-method with the resonant decomposition gives an improvement
Scientific paper
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).
Miao Changxing
Shao Shuanglin
Wu Yifei
Xu Guixiang
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