Stability properties of the Euler-Korteweg system with nonmonotone pressures

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.

References in corpus (1)

• Well/ill posedness for the Euler-Korteweg-Poisson system and related problems

Cited by in corpus (2)

• High-friction limits of Euler flows for multicomponent systems
• On the convergence of the regularized entropy-based moment method for kinetic equations