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arxiv: 1302.6380 · v1 · pith:VY5RZWSBnew · submitted 2013-02-26 · 🧮 math.AP

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

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keywords dimensionsequationmodifiedspacethreezakharov-kuznetsovcauchycombined
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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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