Weighted Hilbert spaces for the stationary exterior Stokes problem with Navier slip boundary conditions

被引：11

作者：

Dhifaoui, Anis ^{[1
,2
]}

Meslameni, Mohamed ^{[3
,4
]}

Razafison, Ulrich ^{[1
]}

机构：

[1] Univ Bourgogne Franche Comte, Lab Math Besancon, CNRS, UMR 6623, 16 Route Gray, F-25030 Besancon, France

[2] Sfax Univ, Fac Sci, Lab Stabil & Control Syst, Sfax, Tunisia

[3] AL Baha Univ, Coll Arts & Sci Al Mandaq, Al Bahah, Saudi Arabia

[4] Univ Sfax, Preparatory Inst Engn Studies Sfax, Sfax, Tunisia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 472卷 / 02期

关键词：

Fluid mechanics; Stokes equations; Navier slip boundary conditions; Exterior domain; Weighted spaces; Korn's inequalities; INVERTED FINITE-ELEMENTS; L-P-THEORY; ELLIPTIC PROBLEMS; EQUATIONS; DECOMPOSITION; REGULARITY; UNIQUENESS; VORTICITY; EXISTENCE; SYSTEMS;

D O I：

10.1016/j.jmaa.2018.12.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we analyze the three-dimensional exterior Stokes problem with the Navier slip boundary conditions, describing the flow of a viscous and incompressible fluid past an obstacle where it is assumed that the fluid may slip at the boundary. Because the flow domain is unbounded, we set the problem in weighted spaces in order to control the behavior at infinity of the solutions. This functional framework also allows to prescribe various behaviors at infinity of the solutions (growth or decay). Existence and uniqueness of solutions are shown in a Hilbert setting which gives the tools for a possible numerical analysis of the problem. Weighted Korn's inequalities are the key point in order to study the variational problem. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1846 / 1871

页数：26

共 52 条

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