Abstract
AbstractIn 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.
Funder
Weierstraß-Institut für Angewandte Analysis und Stochastik, Leibniz-Institut im Forschungsverbund Berlin e.V.
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
Reference29 articles.
1. D. Bothe. On the Maxwell-Stefan approach to multicomponent diffusion. In Progress in Nonlinear differential equations and their Applications 80, pages 81–93. Springer, 2011.
2. D. Bothe and W. Dreyer. Continuum thermodynamics of chemically reacting fluid mixtures. Acta Mech., 226:1757–1805, 2015.
3. D. Bothe, W. Dreyer, and P.-E. Druet. Multicomponent incompressible fluids – An asymptotic study. Preprint, 2021. Available at http://www.wias-berlin.de/preprint/2825/wias_preprints_2825.pdf, and at arXiv:2104.08628 [math-ph].
4. D. Bothe and P.-E. Druet. On the structure of continuum thermodynamical diffusion fluxes: a novel closure scheme and its relation to the Maxwell-Stefan and the Fick-Onsager approach. Preprint, 2020. Available at: http://www.wias-berlin.de/preprint/2749/wias_preprints_2749.pdf and at arXiv:2008.05327 [math-ph].
5. D. Bothe and P.-E. Druet. Mass transport in multicomponent compressible fluids: local and global well-posedness in classes of strong solutions for general class-one models. Nonlinear Analysis, 210:112389, 2021. https://doi.org/10.1016/j.na.2021.112389.
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