Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations

2023/04/08 by Dennis Gallenmüller, Gallenmüller, Dennis, Piotr Gwiazda +5 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2304.04050

Abstract

We consider a combined system of Euler--Korteweg and Euler--Poisson equations with friction and exponential pressure with exponent γ> 1. We show the existence of dissipative measure-valued solutions in the cases of repulsive and attractive potential in Euler--Poisson system. The latter case requires additional restriction on γ. Furthermore in case of γ≥ 2 we show that the strong solutions to the Cahn--Hillard--Keller--Segel system are a high-friction limit of the dissipative measure-valued solutions to Euler--Korteweg--Poisson equations.

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• Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions

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