Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation

被引:54
作者
Ye, Zhuan [1 ]
Xu, Xiaojing [1 ]
机构
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
关键词
2D Boussinesq equations; Fractional Laplacian dissipation; Global regularity; BLOW-UP CRITERION; SMOOTH SOLUTIONS; REGULARITY; MODELS; SYSTEM;
D O I
10.1016/j.jde.2016.01.014
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
As a continuation of the previous work [48], in this paper we focus on the Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation. We give an elementary proof of the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. The argument is based on the nonlinear lower bounds for the fractional Laplacian established in [13]. Consequently, this result significantly improves the recent works [13,45,48]. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码:6716 / 6744
页数:29
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