论文标题
根据弱$ l^3 $ norm的定量控制轴对称的Navier-Stokes方程的解决方案
Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak $L^3$ norm
论文作者
论文摘要
我们关注的是$ 3 $ d不可压缩的Navier-Stokes方程的强轴对称解决方案。我们表明，如果在时间间隔$ [0，t] $上由$ a \ gg 1 $限制的弱$ l^3 $规范$ u $，则每个$ k \ geq 0 $都存在$ c_k> 1 $，这样$ \ | d^k u（t）\ | _ {l^\ infty（\ mathbb {r}^3）} \ leq t^{ - （1+k）/2} \ exp \ exp \ exp a^{c_k} $用于所有$ t \ in（0，t] $。
We are concerned with strong axisymmetric solutions to the $3$D incompressible Navier-Stokes equations. We show that if the weak $L^3$ norm of a strong solution $u$ on the time interval $[0,T]$ is bounded by $A \gg 1$ then for each $k\geq 0 $ there exists $C_k>1$ such that $\| D^k u (t) \|_{L^\infty (\mathbb{R}^3) } \leq t^{-(1+k)/2}\exp \exp A^{C_k}$ for all $t\in (0,T]$.
