Year: 2019
Type: article
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.
Source: Nonlinearity
Authors: Xiaokai Huo, Ansgar Jüngel, Athanasios E Tzavaras
Institutions: King Abdullah University of Science and Technology, TU Wien
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2897315302