High-friction limits of Euler flows for multicomponent systems

Xiaokai Huo, ANSGAR JÜNGEL, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The high-friction limit in Euler-Korteweg equations for fluid mixtures is analyzed. 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.
Original languageEnglish (US)
Pages (from-to)2875-2913
Number of pages39
JournalNonlinearity
Volume32
Issue number8
DOIs
StatePublished - Jul 17 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Part of this manuscript was written during the stay of the second author at the King Abdullah University of Science and Technology (KAUST). He thanks KAUST for the hospitality and support during his stay. Furthermore, he acknowledges partial support from the Austrian Science Fund (FWF), grants F65, P27352, P30000, and W1245.

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