Well-posedness analysis of multicomponent incompressible flow models
Abstract
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities stays constant. In this type of models, the velocity field in the Navier-Stokes equations is not solenoidal and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.
Cite
@article{arxiv.2005.12052,
title = {Well-posedness analysis of multicomponent incompressible flow models},
author = {Dieter Bothe and Pierre-Etienne Druet},
journal= {arXiv preprint arXiv:2005.12052},
year = {2020}
}