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The Zakharov-Kuznetsov equation in spatial dimension $d\geq 5$ is considered.The Cauchy problem is shown to be globally well-posed for small initial data incritical spaces and it is proved that solutions scatter to free solutions as $t\to \pm \infty$. The proof is based on i) novel endpoint non-isotropicStrichartz estimates which are derived from the $(d-1)$-dimensionalSchr\"odinger equation, ii) transversal bilinear restriction estimates, andiii) an interpolation argument in critical function spaces. Under an additionalradiality assumption, a similar result is obtained in dimension $d=4$.

The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity