Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911800269733888 |
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| author | Hurm, Christoph Knopf, Patrik Poiatti, Andrea |
| author_facet | Hurm, Christoph Knopf, Patrik Poiatti, Andrea |
| contents | The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier--Stokes--Cahn--Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the Model H. This means that we show that the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the weight function in the nonlocal interaction kernel approaches the delta distribution. Compared to previous results in the literature, our main novelty is to further establish corresponding convergence rates. Before investigating the nonlocal-to-local convergence, we first need to ensure the strong well-posedness of the nonlocal Model H. In two dimensions, this result can already be found in the literature, whereas in three dimensions, it will be shown in the present paper. Moreover, in both two and three dimensions, we establish suitable uniform bounds on the strong solutions of the nonlocal Model H, which are essential to prove the nonlocal-to-local convergence results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_10947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential Hurm, Christoph Knopf, Patrik Poiatti, Andrea Analysis of PDEs Mathematical Physics Primary: 35Q35. Secondary: 35K55, 35Q30, 45K05, 76D03, 76D05 The main goal of this paper is to establish the nonlocal-to-local convergence of strong solutions to a Navier--Stokes--Cahn--Hilliard model with singular potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the Model H. This means that we show that the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the weight function in the nonlocal interaction kernel approaches the delta distribution. Compared to previous results in the literature, our main novelty is to further establish corresponding convergence rates. Before investigating the nonlocal-to-local convergence, we first need to ensure the strong well-posedness of the nonlocal Model H. In two dimensions, this result can already be found in the literature, whereas in three dimensions, it will be shown in the present paper. Moreover, in both two and three dimensions, we establish suitable uniform bounds on the strong solutions of the nonlocal Model H, which are essential to prove the nonlocal-to-local convergence results. |
| title | Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential |
| topic | Analysis of PDEs Mathematical Physics Primary: 35Q35. Secondary: 35K55, 35Q30, 45K05, 76D03, 76D05 |
| url | https://arxiv.org/abs/2403.10947 |