New asymptotic profiles of nonstationary solutions of the Navier-Stokes system

被引：66

作者：

Brandolese, Lorenzo

Vigneron, Francois

机构：

[1] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France

[2] Ecole Polytech, Ctr Math Laurent Schwartz, CNRS, UMR 7640, F-91128 Palaiseau, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2007年 / 88卷 / 01期

关键词：

asymptotic behavior at infinity; far field asymptotics; upper bound estimates; lower bound estimates; mild solutions to the Navier-Stokes system; peetre weight;

D O I：

10.1016/j.matpur.2007.04.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that solutions u(x, t) of the nonstationary incompressible Navier-Stokes system in R-d (d >= 2) starting from mild decaying data a behave as vertical bar x vertical bar -> infinity as a potential field: [GRAPHICS] where gamma(d) is a constant and [GRAPHICS] is the energy matrix of the flow. We deduce that, for well localized data, and for small t and large enough vertical bar x vertical bar, [GRAPHICS] where the lower bound holds on the complementary of a set of directions, of arbitrary small measure on Sd-1. We also obtain new lower bounds for the large time decay of the weighted-L-p norms, extending previous results of Schonbek, Miyakawa, Bae and Jin. (c) 2007 Elsevier Masson SAS. All rights reserved.

引用

页码：64 / 86

页数：23

共 25 条

[1]

[Anonymous], FUNKC EKVACIOJ

[2] Upper and lower bounds of temporal and spatial decays for the Navier-Stokes equations [J].