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 Cauchy problem for the Keller-Segel system of consumptiontype coupled with the incompressible Euler equations in $\mathbb{R}^2$. Thiscoupled system describes a biological phenomenon in which aerobic bacterialiving in slightly viscous fluids (such as water) move towards a higher oxygenconcentration to survive. We firstly prove the local existence of smoothsolutions for arbitrary smooth initial data. Then we show that these smoothsolutions can be extended globally if the initial density of oxygen issufficiently small. The main ingredient in the proof is the $W^{1,q}$-energyestimate $(q>2)$ motivated by the partially inviscid two-dimensional Boussinesqsystem in \cite{C06}. Our result improves the well-known global well-posednessof the two-dimensional Keller-Segel system of consumption type coupled with theincompressible Navier-Stokes equations.

Global well-posedness for a two-dimensional Keller-Segel-Euler system of consumption type