The planar Dirichlet problem for the Stokes equations

被引：1

作者：

Medkova, Dagmar ^{[2
]}

Varnhorn, Werner ^{[1
]}

机构：

[1] Univ Kassel, Fac Math, D-34109 Kassel, Germany

[2] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2011年 / 34卷 / 09期

关键词：

Stokes system; single-layer potential; double-layer potential; BOUNDARY-VALUE-PROBLEMS; SYSTEM; DOMAINS;

D O I：

10.1002/mma.1425

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Dirichlet problem for the Stokes equations is studied in a planar domain. We construct a solution of this problem in form of appropriate potentials and determine the unknown source densities via integral equation systems on the boundary of the domain. The solution is given explicitly in the form of a series. As a consequence we determine a solution of the Dirichlet problem for a compressible Stokes system and a solution of a boundary value problem on a domain with cracks. Copyright (C) 2011 John Wiley & Sons, Ltd.

引用

页码：1097 / 1109

页数：13

共 22 条

[1] Very weak, generalized and strong solutions to the Stokes system in the half-space [J].

Amrouche, Cherif ;

Necasova, Sarka ;

Raudin, Yves .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (04) :887-915

[2]

[Anonymous], 1989, GRADUATE TEXTS MATH

[3] MIXED BOUNDARY VALUE PROBLEMS FOR THE STOKES SYSTEM [J].

Brown, R. ;

Mitrea, I. ;

Mitrea, M. ;

Wright, M. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (03) :1211-1230

[4]

Deuring P, 1998, INDIANA U MATH J, V47, P11

[5] THE DIRICHLET PROBLEM FOR THE STOKES SYSTEM ON LIPSCHITZ-DOMAINS [J].

FABES, EB ;

KENIG, CE ;

VERCHOTA, GC .

DUKE MATHEMATICAL JOURNAL, 1988, 57 (03) :769-793

[6]

Hsiao GC, 2008, APPL MATH SCI, V164, P1

[7]

Kohr M., 2006, APPL ANAL, V85, P1343

[8] Boundary value problems for a compressible Stokes system in bounded domains in Rn [J].

Kohr, Mirela .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 201 (01) :128-145

[9]

Kozlov VA, 1997, MATH METHOD APPL SCI, V20, P315, DOI 10.1002/(SICI)1099-1476(19970310)20:4<315::AID-MMA861>3.0.CO

[10]

2-M

← 1 2 3 →