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

This paper addresses the issue of global existence of so-called$\kappa$-entropy solutions to the Navier-Stokes equations for viscouscompressible and barotropic fluids with degenerate viscosities. We consider thethree dimensional space domain with periodic boundary conditions. Our solutionssatisfy the weak formulation of the mass and momentum conservation equationsand also a generalization of the BD-entropy identity called: $\kappa$-entropy.This new entropy involves a mixture parameter $\kappa \in (0,1)$ between thetwo velocities $\bf{u}$ and $\bf{u} + 2\nabla\varphi(\varrho)$ (the latter wasintroduced by the first two authors in [C. R. Acad. Sci. Paris 2004]), where$\bf{u}$ is the velocity field and $\varphi$ is a function of the density$\varrho$ defined by $\varphi'(s)=\mu'(s)/s$. As a byproduct of the existenceproof, we show that two-velocity hydrodynamics (in the spirit of S.C. Shugrin1994) is a possible formulation of a model of barotropic compressible flow withdegenerate viscosities. It is used in construction of approximate solutionsbased on a conservative augmented approximate scheme.

Two-velocity hydrodynamics in fluid mechanics: Part II Existence of  global $\kappa$-entropy solutions to compressible Navier-Stokes systems with  degenerate viscosities