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arXiv · 1611.01663

Stability properties of the Euler-Korteweg system with nonmonotone pressures

Jan Giesselmann·Athanasios E. Tzavaras
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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.

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Jan Giesselmann, Athanasios E. Tzavaras. 2016-11-05. Stability properties of the Euler-Korteweg system with nonmonotone pressures. https://doi.org/10.1080/00036811.2016.1276175

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