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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.11892 |
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| _version_ | 1866908654623522816 |
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| author | Abels, Helmut Marveggio, Alice Poiatti, Andrea |
| author_facet | Abels, Helmut Marveggio, Alice Poiatti, Andrea |
| contents | We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by means of maximal regularity and contraction mapping arguments. We introduce a suitable entropic weak formulation of the problem, replacing the heat equation by the total energy inequality and an entropy production inequality, and we rigorously prove global-in-time existence of such weak solutions, developing a novel approximation scheme. We also show that an entropic weak solution to this non-isothermal phase-field model converges to a distributional (or $BV$) solution to a non-isothermal Navier--Stokes/mean curvature flow, under an energy convergence assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness and sharp interface limit of a non-isothermal Navier--Stokes/Allen--Cahn model Abels, Helmut Marveggio, Alice Poiatti, Andrea Analysis of PDEs 35K57, 35Q30, 35A01, 35K20, 35K61, 35D35, 35D30, 53E10 We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by means of maximal regularity and contraction mapping arguments. We introduce a suitable entropic weak formulation of the problem, replacing the heat equation by the total energy inequality and an entropy production inequality, and we rigorously prove global-in-time existence of such weak solutions, developing a novel approximation scheme. We also show that an entropic weak solution to this non-isothermal phase-field model converges to a distributional (or $BV$) solution to a non-isothermal Navier--Stokes/mean curvature flow, under an energy convergence assumption. |
| title | Well-posedness and sharp interface limit of a non-isothermal Navier--Stokes/Allen--Cahn model |
| topic | Analysis of PDEs 35K57, 35Q30, 35A01, 35K20, 35K61, 35D35, 35D30, 53E10 |
| url | https://arxiv.org/abs/2511.11892 |