Long-time asymptotics of Navier-Stokes and vorticity equations in a three-dimensional layer

被引：2

作者：

Roussier-Michon, V ^{[1
]}

机构：

[1] Inst Natl Sci Appl, Dpt GMM, Lab MIP, F-31077 Toulouse 4, France

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2004年 / 29卷 / 9-10期

关键词：

Navier-Stokes equation; long-time asymptotics; three dimensional layer; self-similar variables;

D O I：

10.1081/PDE-200037768

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the long-time behavior of solutions of the Navier-Stokes equation in R-2 X (0, 1). After introducing self-similar variables, we compute the long-time asymptotics of the vorticity up to second order, assuming that the initial vorticity is sufficiently small and has polynomial decay at infinity. Afterwards, we relax this smallness assumption and we prove again that the long-time behavior of global bounded solutions is governed by the two-dimensional Navier-Stokes equation. In particular, we show that solutions converge towards Oseen vortices.

引用

页码：1555 / 1605

页数：51

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