# American Institute of Mathematical Sciences

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

 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.
Citation: Zhaohui Huo, Boling Guo. The well-posedness of Cauchy problem for the generalized nonlinear dispersive equation. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 387-402. doi: 10.3934/dcds.2005.12.387
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