论文标题
leray-hopf弱解决方案的部分规律性与不可压缩的Navier-Stokes方程式
Partial regularity of Leray-Hopf weak solutions to the incompressible Navier-Stokes equations with hyperdissipation
论文作者
论文摘要
我们表明，如果$ u $是不可压缩的Navier的LERAY-HOPF弱解决方案 - 用（1,5/4）$ in（1,5/4）$的超级降低$α\ Stoking stokations $ s \ subset \ subset \ mathbb {r}^3 $中存在一个$ y $ y y $ s $ s y Is $ subl yes $ s in $ s $ s y y hausd hausdor for，dim $ s in y hausd of y hausd of y hausd of y hausd of，它的盒子计数尺寸由$（-16α^2 +16α + 5）/3 $界定。我们的方法灵感来自Katz＆Pavlović（Geom。Funct。Anal。，2002）的思想。
We show that if $u$ is a Leray-Hopf weak solution to the incompressible Navier--Stokes equations with hyperdissipation $α\in (1,5/4)$ then there exists a set $S\subset \mathbb{R}^3$ such that $u$ remains bounded outside of $S$ at each blow-up time, the Hausdorff dimension of $S$ is bounded above by $ 5-4α$ and its box-counting dimension is bounded by $(-16α^2 + 16α+5)/3$. Our approach is inspired by the ideas of Katz & Pavlović (Geom. Funct. Anal., 2002).
