Remarks on global regularity of the 2D Boussinesq equations with fractional dissipation

被引：13
|
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
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 125卷
关键词：
2D Boussinesq equations; Fractional dissipation; Global regularity; WELL-POSEDNESS; MAXIMUM PRINCIPLE; SMOOTH SOLUTIONS; LIFE-SPAN; SYSTEM; CRITERION; MODELS;
D O I：
10.1016/j.na.2015.06.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are interested in the study of the Cauchy problem to the two-dimensional (2D) incompressible Boussinesq equations with fractional dissipation. By making use of the nonlinear lower bounds for the fractional Laplacian established in Constantin and Vicol (2012), we establish the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. This result significantly improves the recent works of Constantin and Vicol (2012) and Yang et al. (2014). (C) 2015 Elsevier Ltd. All rights reserved.
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页码：715 / 724
页数：10
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