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

This paper aims at the global regularity problem concerning the 2Dincompressible Boussinesq equations with general critical dissipation. Thecritical dissipation refers to $\alpha +\beta=1$ when $\Lambda^\alpha \equiv(-\Delta)^{\frac{\alpha}{2}}$ and $\Lambda^\beta$ represent the fractionalLaplacian dissipation in the velocity and the temperature equations,respectively. We establish the global regularity for the general case with$\alpha+\beta=1$ and $0.9132\approx \alpha_0<\alpha<1$. The cases when$\alpha=1$ and when $\alpha=0$ were previously resolved by Hmidi, Keraani andRousset \cite{HKR1,HKR2}. The global existence and uniqueness is achieved hereby exploiting the global regularity of a generalized critical surfacequasi-gesotrophic equation as well as the regularity of a combined quantity ofthe vorticity and the temperature.

The 2D incompressible Boussinesq equations with general critical dissipation