On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra

被引：8

作者：

Otarola, Enrique ^{[1
]}

Salgado, Abner J. ^{[2
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso, Chile

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

NUMERISCHE MATHEMATIK | 2022年 / 151卷 / 01期

关键词：

FINITE-ELEMENT APPROXIMATION; SHEAR-DEPENDENT VISCOSITY; NAVIER-STOKES EQUATIONS; BOUNDARY-VALUE-PROBLEMS; DECOMPOSITION TECHNIQUE; LADYZHENSKAYA MODEL; DIRICHLET PROBLEM; REGULARITY; SYSTEM; FLOW;

D O I：

10.1007/s00211-022-01272-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Stokes problem over convex polyhedral domains on weighted Sobolev spaces. The weight is assumed to belong to the Muckenhoupt class A(q) for q is an element of(1, infinity). We show that the Stokes problem is well-posed for all q. In addition, we show that the finite element Stokes projection is stable on weighted spaces. With the aid of these tools, we provide well-posedness and approximation results to some classes of non-Newtonian fluids.

引用

页码：185 / 218

页数：34

共 45 条

[21] SOME INVERSE AND SIMULTANEOUS APPROXIMATION THEOREMS IN WEIGHTED VARIABLE EXPONENT LEBESGUE SPACES
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[22] Some approximation problems for (α, ψ)-differentiable functions in weighted variable exponent lebesgue spaces
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[26] Some questions of harmonic analysis in weighted Morrey type spaces
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[27] Some questions of harmonic analysis in weighted Morrey type spaces
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[28] Some results over thin-thick sets in cone locally convex spaces
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[29] Some results over thin-thick sets in cone locally convex spaces
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[30] ANALYSIS OF POLYMERIC FLOW MODELS AND RELATED COMPACTNESS THEOREMS IN WEIGHTED SPACES
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SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (03) : 1179 - 1215

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