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arXiv · 2304.04050

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

Dennis Gallenmüller·Piotr Gwiazda·Agnieszka Świerczewska-Gwiazda·Jakub Woźnicki
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Abstract

We consider a combined system of Euler--Korteweg and Euler--Poisson equations with friction and exponential pressure with exponent $\gamma > 1$. 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 $\gamma$. Furthermore in case of $\gamma \geq 2$ 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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Dennis Gallenmüller, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Jakub Woźnicki. 2023-04-08. Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations. https://arxiv.org/abs/2304.04050

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