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 50 条

[1] On a problem for the Navier–Stokes equations with the infinite Dirichlet integral
Piotr B. Mucha
[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 2005, 56 : 439 - 452
[2] Solving the Dirichlet problem for Navier–Stokes equations by probabilistic approach
G. N. Milstein
M. V. Tretyakov
[J]. BIT Numerical Mathematics, 2012, 52 : 141 - 153
[3] On a problem for the Navier-Stokes equations with the infinite Dirichlet integral
Mucha, PB
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2005, 56 (03): : 439 - 452
[4] Dirichlet problem for the Stokes equations outside open curves on the plane
Krutitskii, P. A.
[J]. DIFFERENTIAL EQUATIONS, 2008, 44 (09) : 1203 - 1217
[5] Dirichlet problem for the Stokes equations outside open curves on the plane
P. A. Krutitskii
[J]. Differential Equations, 2008, 44 : 1203 - 1217
[6] Solving the Dirichlet problem for Navier-Stokes equations by probabilistic approach
Milstein, G. N.
Tretyakov, M. V.
[J]. BIT NUMERICAL MATHEMATICS, 2012, 52 (01) : 141 - 153
[7] Dirichlet problem for the Stokes equation
V. V. Pukhnachev
[J]. Mathematical Notes, 2017, 101 : 132 - 136
[8] Dirichlet Problem for the Stokes Equation
Pukhnachev, V. V.
[J]. MATHEMATICAL NOTES, 2017, 101 (1-2) : 132 - 136
[9] Global existence of solutions of the Dirichlet problem for the compressible Navier-Stokes equations
Mucha, PB
Zajaczkowski, WM
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2004, 84 (06): : 417 - 424
[10] The Dirichlet Problem for Viscous Compressible Isothermal Navier–Stokes Equations in Two Dimensions
J. Frehse
M. Steinhauer
W. Weigant
[J]. Archive for Rational Mechanics and Analysis, 2010, 198 : 1 - 12

← 1 2 3 4 5 →