Bothe, Dieter ; Druet, Pierre-Etienne (2021)
Well-posedness analysis of multicomponent incompressible flow models.
In: Journal of Evolution Equations, 21 (4)
doi: 10.1007/s00028-021-00712-3
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2021 |
| Creators: | Bothe, Dieter ; Druet, Pierre-Etienne |
| Type of entry: | Bibliographie |
| Title: | Well-posedness analysis of multicomponent incompressible flow models |
| Language: | English |
| Date: | 2021 |
| Place of Publication: | Basel |
| Publisher: | Springer International Publishing |
| Journal or Publication Title: | Journal of Evolution Equations |
| Volume of the journal: | 21 |
| Issue Number: | 4 |
| DOI: | 10.1007/s00028-021-00712-3 |
| Corresponding Links: | |
| 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. |
| Uncontrolled Keywords: | Multicomponent flow, Complex fluid, Fluid mixture, Incompressible fluid, Low Mach-number, Strong solutions |
| Additional Information: | Mathematics Subject Classification: 35M33, 35Q30, 76N10, 35D35, 35B65, 35B35, 35K57, 35Q35, 35Q79, 76R50, 80A17, 80A32, 92E20 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Analysis 04 Department of Mathematics > Analysis > Mathematical Modeling and Analysis |
| Date Deposited: | 05 Sep 2024 08:50 |
| Last Modified: | 05 Sep 2024 08:50 |
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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)
- Well-posedness analysis of multicomponent incompressible flow models. (deposited 05 Sep 2024 08:50) [Currently Displayed]
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