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 $s \gt \frac{1}{2}$. Combined with the conservation of mass and energy this result implies global well-posedness for small data in $H^1(\mathbb{R}^3)$.

Keywords

modified Zakharov-Kuznetsov equation, local and global wellposedness, Fourier restriction norm method

2010 Mathematics Subject Classification

Primary 35Q53. Secondary 37K40.

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Accepted 18 November 2013

Published 25 July 2014