Existence, asymptotic behaviour and convergence of a generalised 3D Muskat problem in stable regime
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911521749073920 |
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| author | Khan, Qasim Suen, Anthony Tang, Bao Quoc |
| author_facet | Khan, Qasim Suen, Anthony Tang, Bao Quoc |
| contents | We address a generalised three-dimensional $α$-Muskat model that comes from the fluid interface problem given by two incompressible fluids with different densities in the stable regime. We establish local-in-time wellposedness when $α\in[0,1)$ and also prove global-in-time existence for strong solutions when $α\in[0,\frac{1}{2})$ with initial data controlled by explicit constants. We obtain maximum principles for the $L^{\infty}$-norms of both the solutions and their gradients, and we further acquire the corresponding decay rates of these $L^{\infty}$-norms. Finally, some convergence results for strong solutions as $α\to0^+$ are also proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence, asymptotic behaviour and convergence of a generalised 3D Muskat problem in stable regime Khan, Qasim Suen, Anthony Tang, Bao Quoc Analysis of PDEs 76D03, 35Q35, 76W05 We address a generalised three-dimensional $α$-Muskat model that comes from the fluid interface problem given by two incompressible fluids with different densities in the stable regime. We establish local-in-time wellposedness when $α\in[0,1)$ and also prove global-in-time existence for strong solutions when $α\in[0,\frac{1}{2})$ with initial data controlled by explicit constants. We obtain maximum principles for the $L^{\infty}$-norms of both the solutions and their gradients, and we further acquire the corresponding decay rates of these $L^{\infty}$-norms. Finally, some convergence results for strong solutions as $α\to0^+$ are also proved. |
| title | Existence, asymptotic behaviour and convergence of a generalised 3D Muskat problem in stable regime |
| topic | Analysis of PDEs 76D03, 35Q35, 76W05 |
| url | https://arxiv.org/abs/2603.16172 |