Bothe, Dieter ; Druet, Pierre-Etienne (2024)
Well-posedness analysis of multicomponent incompressible flow models.
In: Journal of Evolution Equations, 2021, 21 (4)
doi: 10.26083/tuprints-00023425
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Bothe, Dieter ; Druet, Pierre-Etienne |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Well-posedness analysis of multicomponent incompressible flow models |
| Sprache: | Englisch |
| Publikationsjahr: | 3 September 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2021 |
| Ort der Erstveröffentlichung: | Basel |
| Verlag: | Springer International Publishing |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Evolution Equations |
| Jahrgang/Volume einer Zeitschrift: | 21 |
| (Heft-)Nummer: | 4 |
| DOI: | 10.26083/tuprints-00023425 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23425 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | Multicomponent flow, Complex fluid, Fluid mixture, Incompressible fluid, Low Mach-number, Strong solutions |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-234257 |
| Zusätzliche Informationen: | Mathematics Subject Classification: 35M33, 35Q30, 76N10, 35D35, 35B65, 35B35, 35K57, 35Q35, 35Q79, 76R50, 80A17, 80A32, 92E20 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Analysis 04 Fachbereich Mathematik > Analysis > Mathematische Modellierung und Analysis |
| Hinterlegungsdatum: | 03 Sep 2024 13:43 |
| Letzte Änderung: | 05 Sep 2024 08:47 |
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| Suche nach Titel in: | TUfind oder in Google |
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- Well-posedness analysis of multicomponent incompressible flow models. (deposited 03 Sep 2024 13:43) [Gegenwärtig angezeigt]
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