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April  2005, 12(3): 387-402. doi: 10.3934/dcds.2005.12.387

The well-posedness of Cauchy problem for the generalized nonlinear dispersive equation

Zhaohui Huo 1, and  Boling Guo 2,

1. 

Department of Mathematics, School of Sciences, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China
2. 

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

Received  December 2003 Revised  September 2004 Published  December 2004

The well-posedness of the Cauchy problem for a generalized nonlinear dispersive equation is studied. Local well-posedness for data in $H^s(\mathbb R)(s>-\frac{1}{8})$ and the global result for data in $ L^{2}(\mathbb{R})$ are obtained if $l=2$. Moreover, for $l=3$, the problem is locally well-posed for data in $H^s(s>\frac{1}{4}).$ The main idea is to use the Fourier restriction norm method.
Keywords: [k;Z]-multiplier., the Fourier restriction norm, The generalized nonlinear dispersive equation.
Mathematics Subject Classification: 35Q53, 35Q55, 35E1.
Citation: Zhaohui Huo, Boling Guo. The well-posedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 387-402. doi: 10.3934/dcds.2005.12.387
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