论文标题
Zakharov-Kuznetsov方程的亚临界良好的结果在三个及以上的尺寸
Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
论文作者
论文摘要
空间维度中的Zakharov-Kuznetsov方程式$ d \ geq 3 $。事实证明，在完整的亚临界范围$ s>（d-4）/2 $中，cauchy问题在$ h^s（\ mathbb {r}^d）$中是本地提出的，这是最佳的端点。作为推论的，全球良好的体现在$ l^2（\ mathbb {r}^3）$中，在较小的条件下，在$ h^1中（\ mathbb {r}^4）$，关注。
The Zakharov-Kuznetsov equation in space dimension $d\geq 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s(\mathbb{R}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint. As a corollary, global well-posedness in $L^2(\mathbb{R}^3)$ and, under a smallness condition, in $H^1(\mathbb{R}^4)$, follow.
