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

For the physical vacuum free boundary problem with the sound speed being$C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous near vacuum boundaries of thethree-dimensional compressible Euler equations with damping, the globalexistence of spherically symmetric smooth solutions is proved, which are shownto converge to Barenblatt self-similar solutions of the porous media equationwith the same total masses when initial data are small perturbations ofBarenblatt solutions. The pointwise convergence with a rate of density, theconvergence rate of velocity in supreme norm and the precise expanding rate ofphysical vacuum boundaries are also given by constructing nonlinear functionalswith space-time weights featuring the behavior of solutions in large time andnear the vacuum boundary and the center of symmetry, the nonlinear energyestimates and elliptic estimates.

Global Solutions to the Gas-Vacuum Interface Problem of Isentropic  Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and  Physical Vacuum