Stability properties of the Euler-Korteweg system with nonmonotone pressures

Jan Giesselmann, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy to show that solutions of Euler-Korteweg with convex energy converge to solutions of the Euler system in the vanishing capillarity limit, as long as the latter admits sufficiently regular strong solutions.
Original languageEnglish (US)
Pages (from-to)1528-1546
Number of pages19
JournalApplicable Analysis
Volume96
Issue number9
DOIs
StatePublished - Jan 8 2017

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