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 the presence of vacuum, the physical entropy for polytropic gases behavessingularly and it is thus a challenge to study its dynamics. It is shown inthis paper that the boundedness of the entropy can be propagated up to anyfinite time provided that the initial vacuum presents only at far fields withsufficiently slow decay of the initial density. More precisely, for the Cauchyproblem of the one dimensional heat conductive compressible Navier-Stokesequations, the global well-posedness of strong solutions and uniformboundedness of the corresponding entropy are established, as long as theinitial density vanishes only at far fields with a rate no more than$O(\frac{1}{x^2})$. The main tools of proving the uniform boundedness of theentropy are some singularly weighted energy estimates carefully designed forthe heat conductive compressible Navier-Stokes equations and an elaborate DeGiorgi type iteration technique for some classes of degenerate parabolicequations. The De Giorgi type iterations are carried out to different equationsin establishing the lower and upper bounds of the entropy.

Entropy-bounded solutions to the one-dimensional heat conductive compressible Navier-Stokes equations with far field vacuum