On the well-posedness of two-dimensional Muskat problem with an elastic interface
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915707366670336 |
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| author | Wan, Lizhe Yang, Jiaqi |
| author_facet | Wan, Lizhe Yang, Jiaqi |
| contents | We investigate the two-dimensional Muskat problem with a nonlinear elastic interface, for both one-phase and two-phase scenarios. Following the framework developed by Nguyen [35,36], we demonstrate that the problem is locally well-posed in $H^s$ for $s\geq 2$ for arbitrary initial data. Furthermore, for the one-phase case and the stable two-phase case $(ρ^+ \leq ρ^-)$, we establish global well-posedness for small initial data in $H^s$ when $s> \frac{3}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01374 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the well-posedness of two-dimensional Muskat problem with an elastic interface Wan, Lizhe Yang, Jiaqi Analysis of PDEs 35R35, 35Q35, 35A01, 35A02 We investigate the two-dimensional Muskat problem with a nonlinear elastic interface, for both one-phase and two-phase scenarios. Following the framework developed by Nguyen [35,36], we demonstrate that the problem is locally well-posed in $H^s$ for $s\geq 2$ for arbitrary initial data. Furthermore, for the one-phase case and the stable two-phase case $(ρ^+ \leq ρ^-)$, we establish global well-posedness for small initial data in $H^s$ when $s> \frac{3}{2}$. |
| title | On the well-posedness of two-dimensional Muskat problem with an elastic interface |
| topic | Analysis of PDEs 35R35, 35Q35, 35A01, 35A02 |
| url | https://arxiv.org/abs/2601.01374 |