论文标题
Navier-Stokes方程解决方案的规律性的本地标准
A localized criterion for the regularity of solutions to Navier-Stokes equations
论文作者
论文摘要
Serrin-Prodi-ladyzhenskaya类型$ l^{p，q} $标准是针对不可压缩的Navier-Stokes方程的规律性，这是对Clay数学研究所发布的千年问题的基础，内容涉及不可压缩的N-S方程。在本文中，我们建立了一些本地化的$ l^{p，q} $标准，以定期使用方程。实际上，我们获得了方程解决方案解决方案的一些先验估计，仅取决于某些本地$ l^{p，q} $类型规范。这些本地的$ l^{p，q} $类型规范对于合理的初始值很小，对于全球常规解决方案而言，必须很小。因此，得出本地$ l^{p，q} $类型规范的较小甚至界限是必要且足以肯定地回答千年问题的必要条件。我们的工作提供了一种有趣且合理的方法来研究千年问题。
The Serrin-Prodi-Ladyzhenskaya type $L^{p,q}$ criteria for the regularity of solutions to the incompressible Navier-Stokes equations are fundamental in the study of the millennium problem posted by the Clay Mathematical Institute about the incompressible N-S equations. In this article, we establish some localized $L^{p,q}$ criteria for the regularity of solutions to the equations. In fact, we obtain some a priori estimates of solutions to the equations depend only on some local $L^{p,q}$ type norms. These local $L^{p,q}$ type norms, are small for reasonable initial value and shall remain to be small for global regular solutions. Thus, deriving the smallness or even the boundedness of the local $L^{p,q}$ type norms is necessary and sufficient to affirmatively answer the millennium problem. Our work provides an interesting and plausible approach to study the millennium problem.
