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 study the compressible quantum Navier-Stokes (QNS) equations withdegenerate viscosity in the three dimensional periodic domains. On the onehand, we consider QNS with additional damping terms. Motivated by the recentworks [Li-Xin, arXiv:1504.06826] and [Antonelli-Spirito, Arch. Ration. Mech.Anal., 203(2012), 499--527], we construct a suitable approximate system whichhas smooth solutions satisfying the energy inequality and the BD entropyestimate. Using this system, we obtain the global existence of weak solutionsto the compressible QNS equations with damping terms for large initial data.Moreover, we obtain some new a priori estimates, which can avoid using theassumption that the gradient of the velocity is a well-defined function, whichis indeed used directly in [Vasseur-Yu, SIAM J. Math. Anal., 48 (2016),1489--1511; Invent. Math., 206 (2016), 935--974]. On the other hand, in theabsence of damping terms, we also prove the global existence of weak solutionsto the compressible QNS equations without the lower bound assumption on thedispersive coefficient, which improves the previous result due to[Antonelli-Spirito, Arch. Ration. Mech. Anal., 203(2012), 499--527].

Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity