论文标题
广义Zakharov-Kuznetsov方程的最大功能估计和局部良好性
Maximal function estimates and local well-posedness for the generalized Zakharov--Kuznetsov equation
论文作者
论文摘要
我们证明了与自由Zakharov-Kuznetsov方程相关的单一组的Strichartz估计值的高维版本。作为一个生产，我们推断出最大的估计值，使我们能够在整个亚临界情况下证明局部良好的Zakharov和Kuznetsov方程，每当$ d \ ge 4，k \ ge 4，$补充Kinoshita和herr-yr-kinoshita的最新结果。最后，我们使用其中一些最大估计值，以证明广义Zakharov（Kuznetsov方程）在任何维度上的流动结果，都以Compaan，Lucà和Staffilani最近的手稿的同样精神。
We prove a high-dimensional version of the Strichartz estimates for the unitary group associated to the free Zakharov--Kuznetsov equation. As a by--product, we deduce maximal estimates which allow us to prove local well-posedness for the generalized Zakharov--Kuznetsov equation in the whole subcritical case whenever $d \ge 4, k \ge 4,$ complementing the recent results of Kinoshita and Herr--Kinoshita. Finally, we use some of those maximal estimates in order to prove pointwise convergence results for the flow of the generalized Zakharov--Kuznetsov equation in any dimension, in the same spirit of a recent manuscript by Compaan, Lucà and Staffilani.
