Effective velocity in compressible Navier-Stokes equations with third-order derivatives |
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Authors: | Ansgar Jü ngel |
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Affiliation: | Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien, Austria |
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Abstract: | 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. |
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Keywords: | 35G25 35Q53 35Q40 76Y05 |
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