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Locally Space-Time Anisotropic Regularity Criteria for the Navier–Stokes Equations in Terms of Two Vorticity Components
Journal of Mathematical Fluid Mechanics ( IF 1.2 ) Pub Date : 2021-03-18 , DOI: 10.1007/s00021-020-00544-0
Zdenek Skalak

In this paper we prove the regularity of Leray weak solutions of the Navier–Stokes equations as long as the vorticity projection to a plane is bounded in the scale critical space \(L^p(0,T;L^q)\), \(2/p+3/q=2\), \(q \in (3/2,\infty )\). The plane may vary in space and time while the unit vector \(v=v(x,t)\) orthogonal to the plane is locally a Hölder function in space with the coefficient 1/2. This extends previous works by Chae and Choe and by Miller. We further show that a generalized form of this criterion improves several other regularity criteria in terms of the vorticity direction known from the literature.



中文翻译:

基于两个涡度分量的Navier-Stokes方程的局部时空各向异性正则判据

本文证明了Navier-Stokes方程的Leray弱解的正则性,只要对平面的涡旋投影在尺度临界空间\(L ^ p(0,T; L ^ q)\)内\(2 / p + 3 / q = 2 \)\(q \ in(3/2,\ infty)\)。平面在空间和时间上可能会发生变化,而与平面正交的单位矢量\(v = v(x,t)\)在局部空间上是Hölder函数,系数为1/2。这是蔡和崔以及米勒先前作品的延伸。我们进一步表明,根据文献中已知的涡度方向,该准则的广义形式可以改善其他几个规则性准则。

更新日期:2021-03-18
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