论文标题
在多种多样的2D Navier-Stokes的全球规律性的几何诱捕方法
A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds
论文作者
论文摘要
在本文中，我们使用频率分解技术为Navier-Stokes方程的全局存在和规律性提供了直接证明，该方程在没有边界的二维Riemannian歧管上。我们的技术的灵感来自于Mattingly和Sinai [15]的方法，该方法是在平坦背景下的周期性边界条件下开发的，并且基于傅立叶系数的最大原理。 一般歧管的扩展需要几个新想法，该想法与我们环境中较不利的光谱本地化属性有关。我们的论点利用频率投影算子，起源于非线性schrödinger方程的多线性估计以及微局部分析的思想。
In this paper, we use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without boundary. Our techniques are inspired by an approach of Mattingly and Sinai [15] which was developed in the context of periodic boundary conditions on a flat background, and which is based on a maximum principle for Fourier coefficients. The extension to general manifolds requires several new ideas, connected to the less favorable spectral localization properties in our setting. Our arguments make use of frequency projection operators, multilinear estimates that originated in the study of the non-linear Schrödinger equation, and ideas from microlocal analysis.
