论文标题
Zakharov-Kuznetsov方程在高维度：关键规律性的小初始数据
The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity
论文作者
论文摘要
考虑到空间尺寸$ d \ geq 5 $中的Zakharov-Kuznetsov方程。在关键空间中的小初始数据中，库奇的问题被证明是全球范围的，并且证明解决方案以$ t \ to \ pm \ pm \ infty $散布以散布解决方案。该证明基于i）新型终点非异分strichartz估计值，这些估计来自$（d-1）$ - 尺寸schrödinger方程，ii）横向双线性限制估计，iii）在关键函数空间中的插值参数。在额外的径向假设下，在尺寸$ d = 4 $中获得了类似的结果。
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 in critical 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-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 $d=4$.
