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A. Jüngel:
"Effective velocity in compressible Navier-Stokes equations with third-order derivatives";
Nonlinear Analysis: Theory, Methods and Applications, 74 (2011), 2813 - 2818.

A formulation of certain barotropic compressible Navier-Stokes equations with third-order
derivatives as a viscous Euler system is proposed by using an effective velocity variable.
The equations model, for instance, viscous Korteweg or quantum Navier-Stokes flows. The
formulation in the new variable allows for the derivation of an entropy identity, which is
known as the BD (Bresch-Desjardins) entropy equation. As a consequence of this estimate,
a new global-in-time existence result for the one-dimensional quantum Navier-Stokes
equations with strictly positive particle densities is proved.

Siehe englisches Abstract.

Quantum Navier-Stokes equations; viscous Euler equations; osmotic velocity