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 the series of this paper and the forthcoming papers [41,42] we study theNavier-Stokes equations in a three-dimensional curved thin domain around agiven closed surface under Navier's slip boundary conditions. We focus on thestudy of the Stokes operator for the curved thin domain in this paper. Theuniform norm equivalence for the Stokes operator and a uniform differenceestimate for the Stokes and Laplace operators are established in whichconstants are independent of the thickness of the curved thin domain. To provethese results we show a uniform Korn inequality and a uniform a priori estimatefor the vector Laplace operator on the curved thin domain based on a carefulanalysis of vector fields and surface quantities on the boundary. We alsopresent examples of curved thin domains and vector fields for which the uniformKorn inequality is not valid but a standard Korn inequality holds with aconstant that blows up as the thickness of a thin domain tends to zero.

Navier-Stokes equations in a curved thin domain, Part I: uniform estimates for the Stokes operator