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

It is well known that the Euler vortex patch in $\mathbb{R}^{2}$ will remainregular if it is regular enough initially. In bounded domains, the regularitytheory for patch solutions is less complete. We study here the Euler vortexpatch in a disk. We prove global in time regularity by providing the upperbound of the growth of curvature of the patch boundary. For a special symmetricscenario, we construct an example of double exponential curvature growth,showing that such upper bound is qualitatively sharp.

Global regularity and fast small scale formation for Euler patch equation in a disk