论文标题
从集中到定量规律性：对Navier-Stokes方程的最新发展的简短调查
From concentration to quantitative regularity: a short survey of recent developments for the Navier-Stokes equations
论文作者
论文摘要
在这篇简短的调查论文中，我们关注的一些新发展是研究3D Navier-Stokes方程解决方案的规律性或潜在奇异性形成。一些激励的问题是：某些规范是否积累/集中在潜在爆炸时间附近的小规模上？某些规模不变规范以什么速度爆炸？一个人可以证明明确的定量规律性估计吗？一个人可以稍微打破临界障碍吗？我们强调，这些问题紧密相连。 Navier-Stokes方程的许多最新进展直接受到非线性分散方程领域的结果和方法的启发。
In this short survey paper, we focus on some new developments in the study of the regularity or potential singularity formation for solutions of the 3D Navier-Stokes equations. Some of the motivating questions are: Are certain norms accumulating/concentrating on small scales near potential blow-up times? At what speed do certain scale-invariant norms blow-up? Can one prove explicit quantitative regularity estimates? Can one break the criticality barrier, even slightly? We emphasize that these questions are closely linked together. Many recent advances for the Navier-Stokes equations are directly inspired by results and methods from the field of nonlinear dispersive equations.
