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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: JG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’.