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 are concerned on the study of the unique continuation type property forthe 3D incompressible Euler equations in the self-similar type form. Discretelyself-similar solution is a generalized notion of the self-similar solution,which is equivalent to a time periodic solution of the time dependentself-similar Euler equations. We prove the unique continuation type theorem forthe discretely self-similar solutions to the Euler equations in $\Bbb R^3$.More specifically, we suppose there exists an open set $G\subset \Bbb R^3$containing the origin such that the velocity field $V\in C_s^1C^{2}_y (\BbbR^{3+1})$ vanishes on $G\times (0, S_0)$, where $S_0 > 0$ is the temporalperiod for $V(y,s)$. Then, we show $V(y,s)=0$ for all $(y,s)\in \Bbb R^{3+1}$.Similar property also holds for the inviscid magnetohydrodynamic system

Continuation of the zero set for discretely self-similar solutions to the Euler equations