X. Huo, A. Jüngel, A. Tzavaras:

"High-friction limits of Euler flows for multicomponent systems";

in: "ASC Report 29/2018", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2018, ISBN: 978-3-902627-11-7, 1 - 39.

The high-friction limit in Euler-Korteweg equations for ﬂuid mixtures is an-alyzed. The convergence of the solutions towards the zeroth-order limiting system and the ﬁrst-order correction is shown, assuming suitable uniform bounds. Three results are proved: The ﬁrst-order correction system is shown to be of Maxwell-Stefan type and its diﬀusive part is parabolic in the sense of Petrovskii. The high-friction limit towards the ﬁrst-order Chapman-Enskog approximate system is proved in the weak-strong solution context for general Euler-Korteweg systems. Finally, the limit towards the zeroth-order system is shown for smooth solutions in the isentropic case and for weak-strong solutions in the Euler-Korteweg case. These results include the case of constant capillarities and multicomponent quantum hydrodynamic models.

High-friction limit, relaxation limit, Euler-Korteweg equations, Maxwell-Stefan systems, relative entropy method

http://www.asc.tuwien.ac.at/preprint/2018/asc29x2018.pdf

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