L2-asymptotic stability of singular solutions to the Navier-Stokes system of equations in R3

被引：18

作者：

Karch, Grzegorz ^{[1
]}

Pilarczyk, Dominika ^{[1
]}

Schonbek, Maria E. ^{[2
]}

机构：

[1] Uniwersytet Wroclawski, Inst Matemat, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[2] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2017年 / 108卷 / 01期

基金：

美国国家科学基金会;

关键词：

Navier-Stokes equations; Weak solutions; Asymptotic stability; Fourier splitting; SELF-SIMILAR SOLUTIONS; WEAK SOLUTIONS; LP-SOLUTIONS; L2; DECAY; MULTIPLIERS; UNIQUENESS; SPACES;

D O I：

10.1016/j.matpur.2016.10.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider global-in-time small solutions of the initial value problem to the incompressible Navier-Stokes equations in R-3. Usually, such solutions do not belong to L-2(R-3) and may be singular if they correspond to singular external forces. However, we prove that we can still establish their asymptotic stability under arbitrarily large initial L-2-perturbations. (C) 2016 Elsevier Masson SAS. All rights reserved.

引用

页码：14 / 40

页数：27