On the weighted decay for solutions of the Navier-Stokes system

被引：27

作者：

Kukavica, Igor ^{[1
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 06期

关键词：

Navier-Stokes equation; Time decay; Space decay; Strong solutions; SPACE-TIME DECAY; WEAK SOLUTIONS; ASYMPTOTIC-BEHAVIOR; L2; DECAY; EQUATIONS; LP;

D O I：

10.1016/j.na.2008.03.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the question of to what extent the temporal decay parallel to u(., t)parallel to(L2) = O(t-(gamma 0)) for solutions u of the Navier-Stokes equation influences the decay of weighted norms. We prove that parallel to vertical bar x vertical bar(a)u(., t)parallel to(L2) = O(t(-gamma 0+a/2)) holds under the condition 0 <= a < n/2 + 1. This extends the range of weights obtained in [L Kukavica, JJ. Torres, Weighted L(p) decay for solutions of the Navier-Stokes equations, Commun. Partial Differential Equations 32 (2007) 819-831]. A wider range of exponents is also obtained for the decay of LP norms. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2466 / 2470

页数：5

共 25 条

[1] Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations [J].