On the principal eigenvalue of the Stokes operator in cylindrical domains

被引：1

作者：

Karpinski, Mikolaj ^{[1
]}

Nowakowski, Bernard ^{[2
]}

Strohmer, Gerhard ^{[3
]}

机构：

[1] Polish Acad Sci, Inst Geophys, Warsaw, Poland

[2] Polish Acad Sci, Inst Math, Warsaw, Poland

[3] Univ Iowa, Coll Liberal Arts & Sci, Math Dept, Iowa City, IA USA

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2018年 / 98卷 / 10期

关键词：

cylindrical domain; generalized impermeability boundary conditions; Navier boundary conditions; principal eigenvalue; slip boundary conditions; Stokes system; BOUNDARY-CONDITIONS; ELLIPTIC-OPERATORS; EQUATIONS; LAPLACIAN; EXISTENCE; SYSTEM;

D O I：

10.1002/zamm.201700366

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Stokes operator in periodic, three dimensional cylinders supplemented with four types of the boundary conditions: the zero Dirichlet b.c., the Navier b.c., the slip b.c. and the generalized impermeability b.c. We analyze the relation between the principal eigenvalue of the Stokes operator and the diameter of the base of the cylinder. Since the direct computation of the eigenvalues for the Stokes system is very difficult, we examine the vector-valued Laplacian and then draw some conclusions for the Stokes operator.

引用

页码：1742 / 1753

页数：12

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