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arXiv · 1810.08225

High-friction limits of Euler flows for multicomponent systems

Xiaokai Huo·Ansgar Jüngel·Athanasios E. Tzavaras
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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.

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Xiaokai Huo, Ansgar Jüngel, Athanasios E. Tzavaras. 2018-10-18. High-friction limits of Euler flows for multicomponent systems. https://doi.org/10.1088/1361-6544%2Fab12a6

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