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

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