English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The purpose of this paper is to bring to light a method through which theglobal in time existence for arbitrary large in $H^1$ initial data of a strongsolution to 3D periodic Navier-Stokes equations follows. The method consists ofsubdividing the time interval of existence into smaller sub-intervals carefullychosen. These sub-intervals are chosen based on the hypothesis that for anywavenumber $m$, one can find an interval of time on which the energy quantizedin low-frequency components (up to $m$) of the solution $u$ is lesser than theenergy quantized in high-frequency components (down to $m$) or otherwise theopposite. We associate then a suitable number $m$ to each one of the intervalsand 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.

Global in time existence of strong solution to 3D periodic Navier-Stokes equations