A moving boundary problem for periodic Stokesian Hele-Shaw flows

被引：0
|
作者：
Escher, Joachim [1 ]
Matioc, Bogdan-Vasile [1 ]
机构：
[1] Leibniz Univ Hannover, Inst Appl Math, D-30167 Hannover, Germany
来源：
INTERFACES AND FREE BOUNDARIES | 2009年 / 11卷 / 01期
关键词：
Quasilinear elliptic equation; nonlinear parabolic equation; non-Newtonian fluid; Hele-Shaw flow;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the motion of an incompressible, viscous fluid in a Hele-Shaw cell. The free surface is moving under the influence of gravity and the fluid is modelled using a modified Darcy law for Stokesian fluids. We combine results from the theory of quasilinear elliptic equations, analytic semigroups and Fourier multipliers to prove existence of a unique classical solution to the corresponding moving boundary problem.
引用
收藏
页码：119 / 137
页数：19
相关论文
共 50 条
  • [31] An eigenvalue problem for self-similar patterns in Hele-Shaw flows
    Xiao, Wang
    Feng, Lingyu
    Yang, Fang
    Liu, Kai
    Zhao, Meng
    PHYSICA D-NONLINEAR PHENOMENA, 2024, 469
  • [32] A Hele-Shaw problem for tumor growth
    Mellet, Antoine
    Perthame, Benoit
    Quiros, Fernando
    JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 273 (10) : 3061 - 3093
  • [33] Invariant Geometric Properties in Hele-Shaw Flows
    Paula Curt
    Computational Methods and Function Theory, 2016, 16 : 503 - 513
  • [34] Hele-Shaw flows and related problems - Editorial
    Howison, SD
    Ockendon, JR
    EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 1999, 10 : 511 - 512
  • [35] Polynomial solutions to the Hele-Shaw problem
    Kuznetsova, OS
    SIBERIAN MATHEMATICAL JOURNAL, 2001, 42 (05) : 907 - 915
  • [36] Elastic fingering in rotating Hele-Shaw flows
    Carvalho, Gabriel D.
    Gadelha, Hermes
    Miranda, Jose A.
    PHYSICAL REVIEW E, 2014, 89 (05):
  • [37] Inertial effects on rotating Hele-Shaw flows
    Dias, Eduardo O.
    Miranda, Jose A.
    PHYSICAL REVIEW E, 2011, 83 (04):
  • [38] New bounds for stabilizing Hele-Shaw flows
    Daripa, P
    Pasa, G
    APPLIED MATHEMATICS LETTERS, 2005, 18 (11) : 1293 - 1303
  • [39] Ill-posed Hele-Shaw flows
    Andreucci, D
    Caruso, G
    DiBenedetto, E
    FREE BOUNDARY PROBLEMS: THEORY AND APPLICATIONS, 2004, 147 : 27 - 51
  • [40] Hele-Shaw flows with anisotropic surface tension
    Tian, FR
    APPLIED MATHEMATICS LETTERS, 2003, 16 (05) : 715 - 721
12345