On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

被引：4

作者：

Abe, Takayuki ^{[1
]}

Yamazaki, Masao ^{[2
]}

机构：

[1] Kisarazu Natl Coll Technol, Chiba 2920041, Japan

[2] Waseda Univ, Sch Sci & Engn, Dept Math Sci, Shinjuku Ku, Tokyo 1698555, Japan

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2010年 / 12卷 / 01期

基金：

日本学术振兴会;

关键词：

Stokes equation; stationary problem; infinite layer; Sobolev space; Besov space; homogeneous Besov space; Poiseuille flow;

D O I：

10.1007/s00021-008-0276-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = a. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.

引用

页码：61 / 100

页数：40

共 10 条

[1] On a resolvent estimate of the Stokes equation on an infinite layer
Abe, T
Shibata, Y
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2003, 55 (02) : 469 - 497
[2] On a Resolvent Estimate of the Stokes Equation on an Infinite Layer Part 2, λ=0 Case
Abe, Takayuki
Shibata, Yoshihiro
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2003, 5 (03) : 245 - 274
[3] ABELS H, REDUCED GEN STOKES 1
[4] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1.
AGMON, S
DOUGLIS, A
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) : 623 - 727
[5] [Anonymous], 1976, GRUNDLEHREN MATH WIS
[6] [Anonymous], 2010, Theory of Function Spaces
[7] GENERALIZED RESOLVENT ESTIMATES FOR THE STOKES SYSTEM IN BOUNDED AND UNBOUNDED-DOMAINS
FARWIG, R
SOHR, H
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1994, 46 (04) : 607 - 643
[8] The Asymptotic Properties of the Solution to the Stokes Problem in Domains That Are Layer-Like at Infinity
Nazarov, S. A.
Pileckas, K.
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 1999, 1 (02) : 131 - 167
[9] On the Solvability of the Stokes and Navier-Stokes Problems in the Domains That Are Layer-Like at Infinity
Nazarov, S. A.
Pileckas, K.
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 1999, 1 (01) : 78 - 116
[10] Stein Elias M., 1970, PRINCETON MATH SERIE, V30

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