On a Resolvent Estimate of the Stokes Equation on an Infinite Layer Part 2, λ=0 Case

被引：34

作者：

Abe, Takayuki ^{[1
]}

Shibata, Yoshihiro ^{[1
,2
]}

机构：

[1] Waseda Univ, Sch Sci & Engn, Dept Math Sci, Shinjuku Ku, Ohkubo 3-4-1, Tokyo 1698555, Japan

[2] Waseda Univ, Adv Res Inst Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2003年 / 5卷 / 03期

关键词：

Infinite layer; Stokes resolvent problem; Navier-Stokes equations; time global existence; small initial data; Poiseuille flow; Couette flow;

D O I：

10.1007/s00021-003-0075-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the standard L-p estimate of solutions to the Stokes resolvent problem on an infinite layer in the case where lambda is close to zero (see eq. (1.1)). Combining this result with that in [1], we find that the Stokes operator on an infinite layer generates an analytic semigroup. As an application, we prove the local stability of some steady flows.

引用

页码：245 / 274

页数：30

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