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

This paper addresses the stability and large-time behavior problem on theperturbations near the hydrostatic balance of the two dimensional Boussinesqsystem, taking into account vertical dissipation and horizontal thermaldiffusion. The spatial framework $\Omega$ is defined as $\mathbb{T}\times\mathbb{R}$, where $\mathbb{T}$ spans $[0, 1]$, representingthe 1D periodic box, while $\mathbb{R}$ denotes the whole line. The resultsoutlined in this article confirm the fact that the temperature can actuallyhave a stabilizing effect on the buoyancy-driven fluids. The stability andlong-time behavior issues discussed here are difficult due to the lack of thehorizontal dissipation and vertical thermal diffusion. By formulating in theappropriate energy functional and implementing the orthogonal decomposition ofthe velocity and the temperature into their horizontal averages and oscillationparts, we are able to make up for the missing regularization and establish thenonlinear stability in the Sobolev space $H^2(\Omega)$ and acheive thealgebraic decay rates for the oscillation parts in the $H^1$-norm.

Stability and large-time behavior for the 2D Boussinesq system with vertical dissipation and horizontal thermal diffusion