Incompressible limit for a fluid mixture
Abstract
In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-number limit in rescaled PDEs are investigated. Using the relative energy inequality, we obtain convergence results for the densities and the velocity-field under the condition that the incompressible model possesses a sufficiently smooth solution, which is granted at least for a short time. Moreover, in comparison to single-component flows, uniform estimates and the convergence of the pressure are needed in the multicomponent case because the incompressible velocity field is not divergence-free. We show that certain constellations of the mobility tensor allow to control gradients of the entropic variables and yield the convergence of the pressure in L1.
Cite
@article{arxiv.2204.11001,
title = {Incompressible limit for a fluid mixture},
author = {Pierre-Etienne Druet},
journal= {arXiv preprint arXiv:2204.11001},
year = {2022}
}