论文标题
Navier-Stokes方程的关键规律性标准根据速度的一个方向导数
Critical regularity criteria for Navier-Stokes equations in terms of one directional derivative of the velocity
论文作者
论文摘要
在本文中，我们考虑了整个空间中的3D Navier-Stokes方程。我们研究了一些新的不等式，\ textit {a先验}估计值以速度字段的一个方向导数提供了关键的规律标准，即$ \ partial_3 \ partbf {u} \ in l^p（（0，t）; l^q（l^q（l^q） \ frac {3} {q} = 2，〜\ frac {3} {2} <q \ leq 6 $。此外，我们将$ q $范围扩展而解决方案是轴对称的，即轴对称解决方案$ \ mathbf {m} {u} {u} $在$（0，t] $中是常规的，如果$（0，t] $，如果$ \ partial_3 u^3 \ in l^p（in l^p（0，t）; l^q（（0，t）; l^q（l^q（\ sath q） \ frac {3} {q} = 2，〜\ frac {3} {2} <q <q <\ infty $。
In this paper, we consider the 3D Navier-Stokes equations in the whole space. We investigate some new inequalities and \textit{a priori} estimates to provide the critical regularity criteria in terms of one directional derivative of the velocity field, namely $\partial_3 \mathbf{u} \in L^p((0,T); L^q(\mathbb{R}^3)), ~\frac{2}{p} + \frac{3}{q} = 2, ~\frac{3}{2}<q\leq 6$. Moreover, we extend the range of $q$ while the solution is axisymmetric, i.e. the axisymmetric solution $\mathbf{m}{u}$ is regular in $(0,T]$, if $ \partial_3 u^3 \in L^p((0,T); L^q(\mathbb{R}^3)), ~\frac{2}{p} + \frac{3}{q} = 2, ~\frac{3}{2}<q< \infty$.
