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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let $Q$ be a smooth compact orientable 3--manifold with smooth boundary$\partial Q$. Let $\mathcal{B}$ be the set of exact 2--forms $B\in\Omega^2(Q)$such that $j_{\partial Q}^*B=0$, where $j_{\partial Q}:{\partial Q}\to Q$ isthe inclusion map. The group $\mathcal{D}=\mathrm{Diff}_0(Q)$ ofself-diffeomorphisms of $Q$ isotopic to the identity acts on the set$\mathcal{B}$ by $\mathcal{D}\times\mathcal{B}\to\mathcal{B}$, $(h,B)\mapstoh^*B$. Let $\mathcal{B}^\circ$ be the set of 2--forms $B\in\mathcal{B}$ withoutzeros. We prove that every $\mathcal{D}$--invariant functional$I:\mathcal{B}^\circ\to\mathbb{R}$ having a regular and continuous derivativewith respect to the $C^1$--topology can be locally (and, if $Q=M\times S^1$with $\partial Q\ne\varnothing$, globally on the set of all 2--forms$B\in\mathcal{B}^\circ$ admitting a cross-section isotopic to $M\times\{*\}$)expressed in terms of the helicity.

Helicity is the only invariant of incompressible flows whose derivative is continuous in $C^1$-topology