Global in Time Estimates for Multi-phase Muskat Problem

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Wang, Zirui
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911592295170048
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