Stability of the equilibria for periodic Stokesian Hele-Shaw flows

被引：2

作者：

Escher, Joachim ^{[1
]}

Matioc, Bogdan-Vasile ^{[1
]}

机构：

[1] Leibniz Univ Hannover, Inst Appl Math, Hannover, Germany

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2008年 / 8卷 / 03期

关键词：

steady state; nonlinear parabolic equation; non-Newtonian fluid; Hele-Shaw flow;

D O I：

10.1007/s00028-008-0381-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled by a modified Darcy's law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The purpose of this paper is to identify the steady states of this flow and to study their stability. The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the bottom is constant then the corresponding steady state is asymptotically stable.

引用

页码：513 / 522

页数：10

共 50 条

[21] Hele-Shaw approximation for resin transfer molding [J].

Besson, O ;

Pousin, J .

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2005, 85 (04) :227-241

[22] A numerical study of unstable Hele-Shaw flow [J].

Hansen, EB ;

Rasmussen, H .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 38 (5-6) :217-230

[23] The Hele-Shaw flow and moduli of holomorphic discs [J].

Ross, Julius ;

Nystroem, David Witt .

COMPOSITIO MATHEMATICA, 2015, 151 (12) :2301-2328

[24] Linear instability of viscoelastic interfacial Hele-Shaw flows: A Newtonian fluid displacing an UCM fluid [J].

Hai, Zhiying ;

Daripa, Prabir .

JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 2022, 303

[25] On the non-isothermal, non-Newtonian Hele-Shaw flows in a domain with rough boundary [J].

Nakasato, Jean Carlos ;

Pazanin, Igor ;

Pereira, Marcone Correa .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 524 (01)

[26] Effect of elasticity of a polymer solution on the Hele-Shaw flow [J].

Win Shwe Maw ;

Shingo Fujiwara ;

Tsutomu Takahashi ;

Masataka Shirakashi .

Journal of Visualization, 2004, 7 :119-126

[27] Effect of elasticity of a polymer solution on the hele-shaw flow [J].

Maw, WS ;

Fujiwara, S ;

Takahashi, T ;

Shirakashi, M .

JOURNAL OF VISUALIZATION, 2004, 7 (02) :119-126

[28] Infinite lifetime for the starlike dynamics in Hele-Shaw cells [J].

Gustafsson, B ;

Prokhorov, D ;

Vasil'ev, A .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (09) :2661-2669

[29] Bubble propagation in Hele-Shaw channels with centred constrictions [J].

Franco-Gomez, Andres ;

Thompson, Alice B. ;

Hazel, Andrew L. ;

Juel, Anne .

FLUID DYNAMICS RESEARCH, 2018, 50 (02)

[30] DENSITY-CONSTRAINED CHEMOTAXIS AND HELE-SHAW FLOW [J].

Kim, Inwon ;

Mellet, Antoine ;

Wu, Yijing .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 377 (01) :395-429

← 1 2 3 4 5 →