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

We establish new non-uniqueness results for the Euler equations with externalforce on $\mathbb{T}^{d}$ $(d\geq3)$. By introducing a novel alternating convexintegration scheme, we construct non-unique, almost-everywhere smooth,H\"older-continuous solutions with regularity $\frac{1}{2}-$, which is notablyabove the Onsager threshold of $\frac{1}{3}$.  The solutions we construct differ significantly in nature from those whicharise from the recent unstable vortex construction of Vishik; in particular,our solutions are genuinely $d$-dimensional ($d\geq3$), and give non-uniquenessresults for any smooth data. To the best of our knowledge, this is the firstinstance of a convex integration construction above the Onsager exponent.

Convex integration above the Onsager exponent for the forced Euler equations