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 are concerned with the global existence and vanishing dispersion limit ofstrong/classical solutions to the Cauchy problem of the one-dimensionalbarotropic compressible quantum Navier-Stokes equations, which consists of thecompressible Navier-Stokes equations with a linearly density-dependentviscosity and a nonlinear third-order differential operator known as thequantum Bohm potential. The pressure $p(\rho)=\rho^\gamma$ is considered with$\gamma\geq1$ being a constant. We focus on the case when the viscosityconstant $\nu$ and the Planck constant $\varepsilon$ are not equal. Under somesuitable assumptions on $\nu,\varepsilon, \gamma$, and the initial data, weproved the global existence and large-time behavior of strong and classicalsolutions away from vacuum to the compressible quantum Navier-Stokes equationswith arbitrarily large initial data. This result extends the previous ones onthe construction of global strong large-amplitude solutions of the compressiblequantum Navier-Stokes equations to the case $\nu\neq\varepsilon$. Moreover, thevanishing dispersion limit for the classical solutions of the quantumNavier-Stokes equations is also established with certain convergence rates. Theproof is based on a new effective velocity which converts the quantumNavier-Stokes equations into a parabolic system, and some elaborate estimatesto derive the uniform-in-time positive lower and upper bounds on the specificvolume.

Global Existence and Vanishing Dispersion Limit of Strong/Classical  Solutions to the One-dimensional Compressible Quantum Navier-Stokes Equations  with Large Initial Data