June  2009, 24(2): 547-565. doi: 10.3934/dcds.2009.24.547

The Cauchy problem for the 3D Zakharov-Kuznetsov equation

1. 

IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320

2. 

Mathématiques UMR 8628, Université Paris-Sud et CNRS, 91405 0rsay cedex, France

Received  March 2008 Revised  August 2008 Published  March 2009

We prove that the Cauchy problem for the three-dimensional Zakharov-Kuznetsov equation is locally well-posed for data in $H^s(\R^3)$, s > $\frac{9}{8}$.
Citation: Felipe Linares, Jean-Claude Saut. The Cauchy problem for the 3D Zakharov-Kuznetsov equation. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 547-565. doi: 10.3934/dcds.2009.24.547
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