From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

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

Abstract

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.
Fichier principal
Vignette du fichier
2305.01348.pdf (487.59 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

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⟩
16 View
20 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More