论文标题
涡度方向的平衡和3D分数Navier-Stokes方程中的涡度幅度
Balance of the vorticity direction and the vorticity magnitude in 3D fractional Navier-Stokes equations
论文作者
论文摘要
分数Navier-Stokes方程（具有分数Laplacian）在Euler方程（零扩散）和Navier-Stokes方程（完整扩散）之间提供“桥”。最初平滑流程是否可以自发发展奇异性的问题是数学物理学中的一个基本问题，该问题是为从Euler到Navier-Stokes的全部模型开放的。这项工作的目的是提出一个杂种，几何分析的规律性标准，用于解决3D分数Navier-Stokes方程的解决方案，在平均意义上是平衡的涡度方向和涡度幅度之间的平衡，分别是流动流的涡度幅度，关键的几何学和分析性描述。
Fractional Navier-Stokes equations -- featuring a fractional Laplacian -- provide a `bridge' between the Euler equations (zero diffusion) and the Navier-Stokes equations (full diffusion). The problem of whether an initially smooth flow can spontaneously develop a singularity is a fundamental problem in mathematical physics, open for the full range of models -- from Euler to Navier-Stokes. The purpose of this work is to present a hybrid, geometric-analytic regularity criterion for solutions to the 3D fractional Navier-Stokes equations expressed as a balance -- in the average sense -- between the vorticity direction and the vorticity magnitude, key geometric and analytic descriptors of the flow, respectively.
