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Pré-Publication, Document De Travail Année : 2023

From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit

Résumé

Several recent papers considered the high-friction limit for systems arising in fluid mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard equation as a limit of the nonlocal Euler-Korteweg equation using the relative entropy method. Applying the recent result by the first and third author, we also derive rigorously the local degenerate Cahn-Hilliard equation. The proof is formulated for dissipative measure-valued solutions of the nonlocal Euler-Korteweg equation which are known to exist on arbitrary intervals of time. Our work provides a new method to derive equations not enjoying classical solutions via relative entropy method by introducing the nonlocal effect in the fluid equation.
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Dates et versions

hal-04088166 , version 1 (03-05-2023)

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Charles Elbar, Piotr Gwiazda, Jakub Skrzeczkowski, Agnieszká Swierczewska-Gwiazda. From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit. 2023. ⟨hal-04088166⟩
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