Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equations - Archive ouverte HAL Access content directly
Journal Articles Asymptotic Analysis Year : 2022

Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equations

Abstract

We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler-Langevin-Korteweg system, which corresponds to the Euler-Korteweg system of compressible quantum fluids with an isothermal pressure law and a linear drag term with respect to the velocity. In particular, the isothermal feature prevents the energy and the BD-entropy from being positive. Adapting standard approximation arguments we first show the existence of global weak solutions to the defocusing isothermal Navier-Stokes-Langevin-Korteweg system. Introducing a relative entropy function satisfying a Gronwall-type inequality we then perform the inviscid limit to obtain the existence of dissipative solutions of the Euler-Langevin-Korteweg system.
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Dates and versions

hal-02964009 , version 1 (13-10-2020)

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Quentin Chauleur. Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equations. Asymptotic Analysis, 2022, 126 (3-4), pp.255-283. ⟨10.3233/ASY-211681⟩. ⟨hal-02964009⟩
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