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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