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

Considering initial data in $\dot{H}^s$, with $\frac{1}{2} \textless{} s\textless{} \frac{3}{2}$, this paper is devoted to the study of possibleblowing-up Navier-Stokes solutions such that $(T*(u\_{0}) -t)^{\frac{1}{2} (s-\frac{1}{2})} \,\, \| u \|\_{\dot{H}^s}}$ is bounded. Our result is in thespirit of the tremendous works of L. Escauriaza, G. Seregin, and V.$\breve{\mathrm{S}}$ver$\acute{\mathrm{a}}$k and I. Gallagher, G. Koch, F.Planchon, where they proved there is no blowing-up solution which remainbounded in $L^3(R^3)$. The main idea is that if such blowing-up solutionsexist, they satisfy critical properties.

About the possibility of minimal blow up for Navier-Stokes solutions with data in $\dot{H}^s(R^3)$