The low regularity global solutions for the critical generalized KdV equation

Details The low regularity global solutions for the critical generalized KdV equation The low regularity global solutions for the critical generalized KdV equation

2009-08-06

arxiv.org/abs/0908.0782v3

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).

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