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

In a recent research on degenerate points of steady axisymmetric gravityflows with general vorticity, it has been shown that the possible asymptoticsnear any stagnation point must be the "Stokes corner", the "horizontal cusp",or the "horizontal flatness" (Theorem 1.1, Du, Huang, Pu, Commun. Math. Phys.,400, 2137-2179, 2023). In this paper, we focus on the horizontally flatsingularity and show that it is not possible, and therefore the "Stokes corner"and the "cusp" are the only possible asymptotics at the stagnation points. Thebasic idea of our proof relies on a perturbation of the frequency formula forthe two-dimensional problem (Varvaruca, Weiss, Acta Math., 206, 363-403, 2011).Our analysis also suggests that, for steady axisymmetric rotational gravityflows, the singular asymptotic profiles at stagnation points are similar to thescenario observed in two-dimensional waves with vorticity (Varvaruca, Weiss,Ann. I. H. Poincare-AN, 29, 861-885, 2012).

The non-existence of horizontally flat singularity for steady axisymmetric free surface flows near stagnation points