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

We consider the incompressible Euler equations in the half cylinder $\mathbb{R}_{>0}\times\mathbb{T}$. In this domain, any vorticity which isindependent of $x_2$ defines a stationary solution. We prove that such astationary solution is nonlinearly stable in a weighted $L^{1}$ norm involvingthe horizontal impulse, if the vorticity is non-negative and non-increasing in$x_1$. This includes stability of cylindrical patches $\{x_{1}<\alpha\},\;\alpha>0$. The stability result is based on the fact that such a profile is theunique minimizer of the horizontal impulse among all functions with the samedistribution function. Based on stability, we prove existence of vortex patchesin the half cylinder that exhibit infinite perimeter growth in infinite time.

Stability of monotone, non-negative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches