Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equation
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.
Keywords
Cite
@article{arxiv.2010.06863,
title = {Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equation},
author = {Quentin Chauleur},
journal= {arXiv preprint arXiv:2010.06863},
year = {2020}
}