A Remark on the modified Zakharov-Kuznetsov equation in three space dimensions

preprint2013arXivOpen access

The Cauchy Problem for the modified Zakharov-Kuznetsov equation in three space dimensions is shown to be locally well-posed in $H^s(\R^3)$ for $s > \frac12$ . Combined with the conservation of mass and energy this result implies global well-posedness for small data in $H^1(\R^3)$ .

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A Remark on the modified Zakharov-Kuznetsov equation in three space dimensions

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