Journal
APPLICABLE ANALYSIS
Volume 96, Issue 9, Pages 1528-1546Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00036811.2016.1276175
Keywords
Euler-Kortweg system; phase transitions; Cahn-Hiliard equation; 35Q31; 76D45; 76T10
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Funding
- Baden-Wuerttemberg foundation
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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.
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