Stability properties of the Euler-Korteweg system with nonmonotone pressures

Jan Giesselmann; Athanasios Tzavaras

doi:10.1080/00036811.2016.1276175

Stability properties of the Euler-Korteweg system with nonmonotone pressures

Jan Giesselmann, Athanasios Tzavaras

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21 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1528-1546
Number of pages	19
Journal	Applicable Analysis
Volume	96
Issue number	9
DOIs	https://doi.org/10.1080/00036811.2016.1276175
State	Published - Jan 8 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: JG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’.

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10.1080/00036811.2016.1276175

https://repository.kaust.edu.sa/bitstream/10754/621819/5/EK_weakstrong.pdf

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title = "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.",

author = "Jan Giesselmann and Athanasios Tzavaras",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: JG thanks the Baden-Wurttemberg foundation for support via the project {\textquoteright}Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers{\textquoteright}.",

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AU - Giesselmann, Jan

AU - Tzavaras, Athanasios

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: JG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’.

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N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/621819

UR - https://arxiv.org/abs/1611.01663

UR - http://www.scopus.com/inward/record.url?scp=85008600532&partnerID=8YFLogxK

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DO - 10.1080/00036811.2016.1276175

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EP - 1546

JO - Applicable Analysis

JF - Applicable Analysis

IS - 9

ER -

Stability properties of the Euler-Korteweg system with nonmonotone pressures

Abstract

Bibliographical note

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