论文标题
全球规律性用于Navier-Stokes方程的解决方案，足够接近Laplacian的特征。
Global regularity for solutions of the Navier-Stokes equation sufficiently close to being eigenfunctions of the Laplacian
论文作者
论文摘要
在本文中，我们将证明针对Navier的解决方案的新的，刻度的临界规则标准 - 斯托克斯方程，足够接近Laplacian的特征函数。该估计值提高了以前的规律标准，要求对$ u的$ \ dot {h}^α$规范，$，$，$ 2 \ leq leqleqα<\ frac {5} {2} {2}，$，对规则标准，需要在$ \ dot emperdential the sumpportial in commitped中进行$ \ dot norm fors properation in the $ \ dot norm intpertion sympodialition cromportation intpertential in commitped。 $ \ dot {湍流。
In this paper, we will prove a new, scale critical regularity criterion for solutions of the Navier--Stokes equation that are sufficiently close to being eigenfunctions of the Laplacian. This estimate improves previous regularity criteria requiring control on the $\dot{H}^α$ norm of $u,$ with $2\leq α<\frac{5}{2},$ to a regularity criterion requiring control on the $\dot{H}^α$ norm multiplied by the deficit in the interpolation inequality for the embedding of $\dot{H}^{α-2}\cap\dot{H}^α \hookrightarrow \dot{H}^{α-1}.$ This regularity criterion suggests, at least heuristically, the possibility of some relationship between potential blowup solutions of the Navier--Stokes equation and the Kolmogorov-Obhukov spectrum in the theory of turbulence.
