论文标题
全球时间在3D周期性的Navier-Stokes方程中存在强大的解决方案
Global in time existence of strong solution to 3D periodic Navier-Stokes equations
论文作者
论文摘要
本文的目的是揭示一种方法，通过该方法，全球的时间存在于$ h^1 $中的任意范围内的$ h^1 $初始数据的强大解决方案的强大解决方案的初始数据随后是纳维尔 - 斯托克斯方程。该方法包括将存在的时间间隔细分为仔细选择的较小的子媒介。根据以下假设选择了这些子间变速器：对于任何波数$ m $，可以找到一个时间间隔的时间间隔，该时间间隔在低频组件中量化的能量（最多$ m $）的解决方案$ u $要比在高频组件（下降到$ m $）或相反的高频组件（下降到$ m $）的能量要小。我们将合适的数字$ m $与每个间隔相关联，我们证明了在两种提到的情况下均构成了norm $ \ | u（t）\ | _ {h^1} $。可以继续该过程，直到达到存在的最大时间$ t_ {max} $，从而产生了强大解决方案的全局时间。
The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in $H^1$ initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of subdividing the time interval of existence into smaller sub-intervals carefully chosen. These sub-intervals are chosen based on the hypothesis that for any wavenumber $m$, one can find an interval of time on which the energy quantized in low-frequency components (up to $m$) of the solution $u$ is lesser than the energy quantized in high-frequency components (down to $m$) or otherwise the opposite. We associate then a suitable number $m$ to each one of the intervals and we prove that the norm $\|u(t)\|_{H^1}$ is bounded in both mentioned cases. The process can be continued until reaching the maximal time of existence $T_{max}$ which yields the global in time existence of strong solution.
