High-friction limits of Euler flows for multicomponent systems

Xiaokai Huo, ANSGAR JÜNGEL, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

6 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

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