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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we consider a damped Navier-Stokes-Bardina model posed on thewhole three-dimensional. These equations have an important physical motivationand they arise from some oceanic model. From the mathematical point of view,they write down as the well-know Navier-Stokes equations with an additionalnonlocal operator in their nonlinear transport term, and moreover, with anadditional damping term depending of a parameter $\beta>0$. We study first theexistence and uniqueness of global in time weak solutions in the energy space.Thereafter, our main objective is to describe the long time behavior of thesesolutions. For this, we use some tools in the theory of dynamical systems toprove the existence of a global attractor, which is a compact subset in theenergy space attracting all the weak solutions when the time goes to infinity.Moreover, we derive an upper bound for the fractal dimension of the globalattractor associated to these equations.  Finally, we find a range of values for the damping parameter $\beta>0$, wherewe are able to give an acutely description of the internal structure of theglobal attractor. More precisely, we prove that the global attractor onlycontains the stationary (time-independing) solution of the dampedNavier-Stokes-Bardina equations.

On the long-time behavior for a damped Navier-Stokes-Bardina model