The multiphase Muskat problem with equal viscosities in two dimensions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-19 DOI:10.4171/ifb/469

Jonas Bierler, Bogdan–Vasile Matioc

引用次数: 4

Abstract

We study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with equal viscosities in a vertical homogeneous porous medium identified with $\mathbb{R}^2$ under the effect of gravity. We first formulate the governing equations as a strongly coupled evolution problem for the functions that parameterize the sharp interfaces between the fluids. Afterwards we prove that the problem is of parabolic type and establish its well-posedness together with two parabolic smoothing properties. For solutions that are not global we exclude, in a certain regime, that the interfaces come into contact along a curve segment.

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二维等黏度多相穆斯卡问题

研究了三维二维多相Muskat问题，该问题描述了三种黏度相等的非混相流体在垂直均匀多孔介质中，在重力作用下的运动，介质为$\mathbb{R}^2$。我们首先将控制方程表述为参数化流体之间尖锐界面的函数的强耦合演化问题。随后证明了该问题是抛物线型的，并建立了该问题的适定性，并给出了两个抛物线平滑性质。对于非全局的解决方案，我们在一定情况下排除接口沿曲线段接触的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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