The existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary condition

被引：9
作者：
Sin, Cholmin [1 ]
机构：
[1] Acad Sci, Inst Math, Pyongyang, North Korea
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 163卷
关键词：
Nonhomogeneous Dirichlet boundary condition; Electrorheological fluid; Existence; Weak solution; Non-Newtonian fluid; Variable exponent; LIPSCHITZ TRUNCATION; REGULARITY;
D O I：
10.1016/j.na.2017.06.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we show the existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary condition under the condition p(x) > 2n/n+ 2, n = 2, 3. In particular, we improve a priori estimate for weak solutions to the problem with min p(x) < 2, which is an improvement even for constant p. (C) 2017 Published by Elsevier Ltd.
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收藏
页码：146 / 162
页数：17
相关论文
共 27 条
  • [1] [Anonymous], 2014, RHEOLOGY NONNEWTONIA, DOI DOI 10.1007/978-3-319-01053-3
  • [2] [Anonymous], APPL NUMERICAL HARMO
  • [3] [Anonymous], 2015, MONOGRAPHS RES NOTES
  • [4] Antontsev S., 2015, ATLANTIS STUDIES DIF, V4
  • [5] Astarita G, 1974, Principles of non-Newtonian fluid mechanics
  • [6] Boundary regularity for the steady Stokes type flow with shear thickening viscosity
    Bae, Hyeong-Ohk
    Wolf, Joerg
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (11) : 3811 - 3850
  • [7] ON THE STATIONARY QUASI-NEWTONIAN FLOW OBEYING A POWER-LAW
    BLAVIER, E
    MIKELIC, A
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1995, 18 (12) : 927 - 948
  • [8] Stationary electro-rheological fluids: Low order regularity for systems with discontinuous coefficients
    Boegelein, Verena
    Duzaar, Frank
    Habermann, Jens
    Scheven, Christoph
    [J]. ADVANCES IN CALCULUS OF VARIATIONS, 2012, 5 (01) : 1 - 57
  • [9] Solenoidal Lipschitz truncation and applications in fluid mechanics
    Breit, D.
    Diening, L.
    Fuchs, M.
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (06) : 1910 - 1942
  • [10] On Existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index
    Bulicek, Miroslav
    Pustejovska, Petra
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 402 (01) : 157 - 166
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