The Zakharov–Kuznetsov equation in spatial dimension \(d\ge 5\) is considered. The Cauchy problem is shown to be globally well-posed for small initial data in critical spaces, and it is proved that solutions scatter to free solutions as \(t \rightarrow \pm \infty \). The proof is based on i) novel endpoint non-isotropic Strichartz estimates which are derived from the \((d-1)\)-dimensional Schrödinger equation, ii) transversal bilinear restriction estimates, and iii) an interpolation argument in critical function spaces. Under an additional radiality assumption, a similar result is obtained in dimension \(d=4\).

考虑空间维\（d \ ge 5 \）中的Zakharov–Kuznetsov方程。对于关键空间中的少量初始数据，柯西问题表现出全局良好的条件，并且证明了解决方案随着\（t \ rightarrow \ pm \ infty \）散布到自由解决方案上。该证明基于i）新的端点非各向同性Strichartz估计，这些估计是从\（（d-1）\）-维Schrödinger方程得出的； ii）横向双线性限制估计，以及iii）关键函数空间中的插值参数。在附加的半径​​假设下，在尺寸\（d = 4 \）中获得了相似的结果。