Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909070712111104 |
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| author | Abels, Helmut Garcke, Harald Poiatti, Andrea |
| author_facet | Abels, Helmut Garcke, Harald Poiatti, Andrea |
| contents | We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space dimensions and a singular free energy density is shown. Moreover, in two space dimensions global existence for sufficiently regular initial data is proven. In three space dimension, existence of strong solutions locally in time is shown as well as regularization for large times in the absence of exterior forces. Moreover, in both two and three dimensions, convergence to stationary solutions as time tends to infinity is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities Abels, Helmut Garcke, Harald Poiatti, Andrea Analysis of PDEs 35B40, 35B65, 35Q30, 35Q35, 76D03, 76D05, 76D45 We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space dimensions and a singular free energy density is shown. Moreover, in two space dimensions global existence for sufficiently regular initial data is proven. In three space dimension, existence of strong solutions locally in time is shown as well as regularization for large times in the absence of exterior forces. Moreover, in both two and three dimensions, convergence to stationary solutions as time tends to infinity is proved. |
| title | Mathematical Analysis of a Diffuse Interface Model for Multi-Phase Flows of Incompressible Viscous Fluids with Different Densities |
| topic | Analysis of PDEs 35B40, 35B65, 35Q30, 35Q35, 76D03, 76D05, 76D45 |
| url | https://arxiv.org/abs/2308.11813 |