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

This paper concerns the dynamics of a layer of incompressible viscous fluidlying above a rigid plane and with an upper boundary given by a free surface.The fluid is subject to a constant external force with a horizontal component,which arises in modeling the motion of such a fluid down an inclined plane,after a coordinate change. We consider the problem both with and withoutsurface tension for horizontally periodic flows. This problem gives rise toshear-flow equilibrium solutions, and the main thrust of this paper is to studythe asymptotic stability of the equilibria in certain parameter regimes. Weprove that there exists a parameter regime in which sufficiently smallperturbations of the equilibrium at time $t=0$ give rise to global-in-timesolutions that return to equilibrium exponentially in the case with surfacetension and almost exponentially in the case without surface tension. We alsoestablish a vanishing surface tension limit, which connects the solutions withand without surface tension.

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension