Stability properties of the Euler-Korteweg system with nonmonotone pressures
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Computer, Electrical, Mathematical Sciences & Engineering Division
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AbstractWe 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.
SponsorsJG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’.
PublisherInforma UK Limited