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 this paper we study a transport-diffusion model with some logarithmicdissipations. We look for two kinds of estimates. The first one is a maximumprinciple whose proof is based on Askey theorem concerning characteristicfunctions and some tools from the theory of $C_0$-semigroups. The second one isa smoothing effect based on some results from harmonic analysis andsub-Markovian operators. As an application we prove the global well-posednessfor the two-dimensional Euler-Boussinesq system where the dissipation occursonly on the temperature equation and has the form$\frac{\DD}{\log^\alpha(e^4+\DD)}$, with $\alpha\in[0,\frac12]$. This resultimproves the critical dissipation $(\alpha=0)$ needed for global well-posednesswhich was discussed in [15].

On a maximum principle and its application to logarithmically critical Boussinesq system