Degenerate two-phase incompressible flow. II: regularity, stability and stabilization.
type: Item
instance of: scholarly article
title: Degenerate two-phase incompressible flow. II: regularity, stability and stabilization.
zbMATH Open document ID: 1073.35129
DOI: 10.1016/S0022-0396(02)00027-X
published in: Journal of Differential Equations
publication date: 2003-04-02T00:00:00Z
review text: The present paper is dedicated to the analysis of a coupled system of highly degenerate elliptic-parabolic partial differential equations for two-phase incompressible flow in porous media. So, is proved that the saturation (unknown \(s\) from the system) is Hölder continuous both in space and time and the total velocity (unknown \(u\) from the system) is Hölder continuous in space (uniformly in time). On the basis of this regularity result, is established next the stability, and the stabilization. Finally, an example is given to show typical regularity of the saturation. For part I, see \textit{Z. Chen}, J. Differ. Equations 171, No. 2, 203--232 (2001; Zbl 0991.35047).
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 1891246
zbMATH Keywords: Porous medium
zbMATH Keywords: Degenerate elliptic-parabolic system
zbMATH Keywords: Flow equation
zbMATH Keywords: Regularity
zbMATH Keywords: Stability
zbMATH Keywords: Uniqueness
zbMATH Keywords: Stabilization
author: Zhangxin Chen
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
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full work available at URL: s0022-0396(02)00027-x
OpenAlex ID: W2093045844
description: scientific article; zbMATH DE number 1891246