Global in Time Estimates for Multi-phase Muskat Problem
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911592295170048 |
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| author | Wang, Zirui |
| author_facet | Wang, Zirui |
| contents | We establish global-in-time decay estimates for the multi-phase Muskat problem in the case where the density takes exactly n+1 distinct constant values. We first linearize the system around a flat stable configuration, followed by the study of associated linearized operator. The asymptotic behavior at low frequencies of eigenvalues yields the decay rate of (1+t)^{-s/2-1/4} for Wiener norm \|f\|_s, which is slower than the classical case, where the decay rate is (1+t)^{-s+ν}. Afterwards we bound the nonlinear term to close the argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12785 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global in Time Estimates for Multi-phase Muskat Problem Wang, Zirui Analysis of PDEs We establish global-in-time decay estimates for the multi-phase Muskat problem in the case where the density takes exactly n+1 distinct constant values. We first linearize the system around a flat stable configuration, followed by the study of associated linearized operator. The asymptotic behavior at low frequencies of eigenvalues yields the decay rate of (1+t)^{-s/2-1/4} for Wiener norm \|f\|_s, which is slower than the classical case, where the decay rate is (1+t)^{-s+ν}. Afterwards we bound the nonlinear term to close the argument. |
| title | Global in Time Estimates for Multi-phase Muskat Problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.12785 |