On a Hele-Shaw Flow Problem with Free and Solid Boundary Components

被引：1

作者：

Kohr, Mirela ^{[1
]}

Pintea, Cornel ^{[1
]}

机构：

[1] Babes Bolyai Univ, Fac Math & Comp Sci, 1 M Kogalniceanu Str, Cluj Napoca 400084, Romania

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2017年 / 11卷 / 08期

关键词：

Hele-Shaw flow problem; Dirichlet-Neumann boundary value problem; Newtonian and boundary layer potentials; Lipschitz domain; Sobolev spaces; LAPLACE EQUATION; SYSTEMS; REGULARITY; BRINKMAN; STOKES; FLUID;

D O I：

10.1007/s11785-017-0719-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this work is to study a one phase Hele-Shaw fluid flow occupying a time variable domain , due to the injection of the fluid with a constant rate at a single point of the initial domain , and in the presence of a fixed solid body . We show the short time existence and uniqueness of the solution for the corresponding boundary value problem in the three dimensional case and in the absence of surface tension.

引用

页码：1729 / 1746

页数：18

共 50 条

[41] A dynamical mother body in a Hele-Shaw problem
Savina, T. V.
Nepomnyashchy, A. A.
PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (14-15) : 1156 - 1163
[42] Optimal Control by Multipoles in the Hele-Shaw Problem
Lev Lokutsievskiy
Vincent Runge
Journal of Mathematical Fluid Mechanics, 2015, 17 : 261 - 277
[43] Optimal Control by Multipoles in the Hele-Shaw Problem
Lokutsievskiy, Lev
Runge, Vincent
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2015, 17 (02) : 261 - 277
[44] A Hele-Shaw problem and the second Painleve transcendent
Fokas, AS
Tanveer, S
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 124 : 169 - 191
[45] A SIMPLIFIED PROOF FOR A MOVING BOUNDARY-PROBLEM FOR HELE-SHAW FLOWS IN THE PLANE
REISSIG, M
VONWOLFERSDORF, L
ARKIV FOR MATEMATIK, 1993, 31 (01): : 101 - 116
[46] TRANSLATION SOLUTIONS OF PROBLEM OF SLOW DIPHASE FLOW IN A HELE-SHAW CANAL
BATAILLE, J
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1968, 266 (15): : 785 - &
[47] Asymptotic properties of solutions to the Hele-Shaw problem
Kuznetsova, OS
Tkachev, VG
DOKLADY AKADEMII NAUK, 1999, 367 (02) : 164 - 165
[48] Asymptotic convergence of the Stefan problem to Hele-Shaw
Quirós, F
Vázquez, JL
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 353 (02) : 609 - 634
[49] FLOW NEAR BOUNDARIES IN A HELE-SHAW MODEL
THIRRIOT, C
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1969, 269 (24): : 1167 - &
[50] Parallel flow in Hele-Shaw cells with ferrofluids
Miranda, JA
Widom, M
PHYSICAL REVIEW E, 2000, 61 (02): : 2114 - 2117

← 1 2 3 4 5 →