A class of solutions of the Navier-Stokes equations with large data

被引：8

作者：

Kukavica, Igor ^{[1
]}

Rusin, Walter ^{[2
]}

Ziane, Mohammed ^{[1
]}

机构：

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

[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 255卷 / 07期

基金：

美国国家科学基金会;

关键词：

Navier-Stokes equations; Weak solutions; Strong solutions; Regularity; REGULARITY; POSEDNESS;

D O I：

10.1016/j.jde.2013.05.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with global regularity of solutions in a periodic domain Q = [0, 1](3). We prove that, in the class of solutions oscillating in the vertical direction, the solutions are smooth under natural conditions on the horizontal derivatives of the horizontal components of the velocity, the derivative in the vertical direction and the vertical average of the initial data. The obtained conditions admit data whose BMO-1-norm has algebraic dependence on 1/h where h is the period of oscillation and generate global solutions. Also, the results allow non-zero force and large data which do not decay in time. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：1492 / 1514

页数：23

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