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

We consider the 3D viscous primitive equations with periodic boundaryconditions. These equations arise in the study of ocean dynamics and generate adynamical system in a Sobolev H^1 type space. Our main result establishes theso-called squeezing property in the Ladyzhenskaya form for this system. As aconsequence of this property we prove (i) the finiteness of the fractaldimension of the corresponding global attractor, (ii) the existence of finitenumber of determining modes, and (iii) ergodicity of a related random kickmodel. All these results provide a new information concerning long timedynamics of oceanic motions.

A squeezing property and its applications to a description of long time behaviour in the 3D viscous primitive equations