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arXiv · 2604.12785

Global in Time Estimates for Multi-phase Muskat Problem

Zirui Wang
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Abstract

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+\nu}. Afterwards we bound the nonlinear term to close the argument.

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Zirui Wang. 2026-04-14. Global in Time Estimates for Multi-phase Muskat Problem. https://arxiv.org/abs/2604.12785

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