三维Navier-Stokes方程在Lorentz空间中的正则性准则

摘要/Abstract

摘要：

该文证明了三维Navier-Stokes方程弱解在尺度不变Lorentz空间中的正则性准则，这些准则依赖于速度或涡度或速度的梯度的水平分量.该结果改进了Navier-Stokes方程的所有已知的关于Lorentz空间或两个分量的正则性准则.

关键词: Navier-Stokes方程, 弱解, 正则性

Abstract:

We prove regularity criteria for weak solutions to the three dimensional Navier-Stokes equations, via horizontal part of the velocity, or the vorticity, or the gradient of velocity in scaling invariant Lorentz spaces. Our results improve almost all known regularity criteria involving Lorentz spaces or two components.

Key words: Navier-Stokes equations, Weak solutions, Regularity

中图分类号:

O175

周道国. 三维Navier-Stokes方程在Lorentz空间中的正则性准则[J]. 数学物理学报, 2021, 41(5): 1396-1404.

Daoguo Zhou. Regularity Criteria in Lorentz Spaces for the Three Dimensional Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1396-1404.

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