论文标题
通过一个速度组件的Navier-Stokes方程来缩放不变的锯齿蛋白标准
Scaling invariant Serrin criterion via one velocity component for the Navier-Stokes equations
论文作者
论文摘要
在本文中，我们证明了leray弱解决方案$ u：\ mathbb {r}^3 \ times（0，t）\ rightArrow \ rightArrow \ mathbb {r}^3 $ navier-stokes方程在$ \ mathbb {rmathbb {r}^3 \ times（0，t）$ serriant novel in actariant in actriant in actriant concortion中是常规的。 $ u_3 \ in l^{q，1}（0，t; t; l^p（\ mathbb {r}^3））$ with \ [\ frac {\ frac {2} {q} {q}+\ frac {3} {p} {p} {p} \ leq 1，\ quad 3 <p <p <+\ \ \ \ \ \ \ \ \ \ f。 \]这个结果是新的局部规则标准的直接结果，该标准是适合弱解决方案的一个速度组件。
In this paper, we prove that the Leray weak solution $u : \mathbb{R}^3\times (0, T)\rightarrow\mathbb{R}^3 $ of the Navier-Stokes equations is regular in $\mathbb{R}^3\times (0,T)$ under the scaling invariant Serrin condition imposed on one component of the velocity $u_3\in L^{q,1}(0, T;L^p(\mathbb{R}^3))$ with \[ \frac{2}{q}+\frac{3}{p}\leq 1,\quad 3<p<+\infty. \] This result is an immediate consequence of a new local regularity criterion in terms of one velocity component for suitable weak solutions.
