论文标题
构建与不可压缩流和应用产生的偏斜缸有关的最大功能
Construction of Maximal Functions associated with Skewed Cylinders Generated by Incompressible Flows and Applications
论文作者
论文摘要
我们构建了与偏斜缸系列相关的最大功能。这些圆柱体被定义为流动流动流的轨迹的管状邻域，出现在流体方程的研究中，例如Navier-Stokes方程和Euler方程。我们将最大功能从属于这些气缸，并表明它是薄型$（1，1）$和强型$（p，p）$的类型薄弱的函数。作为应用程序，我们为三维Navier-Stokes方程的平滑解决方案的较高衍生品估计提供了替代证明。
We construct a maximal function associated with a family of skewed cylinders. These cylinders, which are defined as tubular neighborhoods of trajectories of a mollified flow, appear in the study of fluid equations such as the Navier-Stokes equations and the Euler equations. We define a maximal function subordinate to these cylinders, and show it is of weak type $(1, 1)$ and strong type $(p, p)$ by a covering lemma. As an application, we give an alternative proof for the higher derivatives estimate of smooth solutions to the three-dimensional Navier-Stokes equations.
