On the Stokes semigroup in some non-Helmholtz domains

被引：11

作者：

Abe, Ken ^{[1
]}

Giga, Yoshikazu ^{[2
]}

Schade, Katharina ^{[3
]}

Suzuki, Takuya ^{[2
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

[3] Tech Univ Darmstadt, Fachbereich Math, D-64298 Darmstadt, Germany

来源：

ARCHIV DER MATHEMATIK | 2015年 / 104卷 / 02期

基金：

日本学术振兴会;

关键词：

Sector-like domain; Helmholtz decomposition; Neumann problem; Weighted estimate; RESOLVENT ESTIMATE; OPERATOR; ANALYTICITY; EQUATION; SPACES;

D O I：

10.1007/s00013-015-0729-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper shows that the L (p) -Helmholtz decomposition is not necessary to establish the analyticity of the Stokes semigroup in C (0,sigma) , the L (a)-closure of the space of all compactly supported smooth solenoidal vector fields. In fact, in a sector-like domain for which the L (p) -Helmholtz decomposition does not hold, the analyticity of the Stokes semigroup in C (0,sigma) is proved.

引用

页码：177 / 187

页数：11

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