Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations | |
Yang JQ(杨佳琦) | |
发表期刊 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
2019-10-15 | |
卷号 | 478期号:2页码:1020-1026 |
ISSN | 0022-247X |
摘要 | Recently, by using the argument of Lei & Lin (2011) [11], Liu & Gao (2017) [13] establish the global well-posedness of mild solutions to the three-dimensional Boussinesq equations in the space chi(-1) defined by chi(-1) = {u is an element of D'(R-3) : integral(R3) vertical bar xi vertical bar(-1)vertical bar(xi) over cap (-1)vertical bar xi < infinity < col. However, it seems that their proof is incorrect, and has some obvious and essential mistakes. Compared with the Navier-Stokes equations, it is difficulty to obtain a global well-posedness of mild solutions to the Boussinesq system in the space chi(-1). In this paper, we will point out the mistakes of Liu Sz Gao. And, furthermore, in order to understand the difficulty of the Boussinesq system better, we study an illuminating system as follows: {partial derivative(t)u + (u . del)u - mu(1 + t)(alpha) del u + del p = theta e(3), in R-3 x (0, infinity), partial derivative(t)theta + (u . del)theta - k (1 + t)(alpha) Delta theta, in R-3 x (0, infinity), del . u = 0, in R-3 x (0, infinity), u(x, 0) = u(0), theta(x,0) = theta degrees, in R-3, where mu > 0, k > 0 and alpha > 1 are real constant parameters. By using the time-weighted estimate, we can show that the above system has a global mild solution. (C) 2019 Elsevier Inc. All rights reserved. |
关键词 | Boussinesq equations Global well-posedness Mild solutions |
DOI | 10.1016/j.jmaa.2019.05.063 |
收录类别 | SCI |
语种 | 英语 |
WOS记录号 | WOS:000475547900036 |
关键词[WOS] | TIME DECAY |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics, Applied ; Mathematics |
论文分区 | 二类 |
力学所作者排名 | 1 |
RpAuthor | Yang, Jiaqi |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://dspace.imech.ac.cn/handle/311007/79473 |
专题 | 流固耦合系统力学重点实验室 |
推荐引用方式 GB/T 7714 | Yang JQ. Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2019,478,2,:1020-1026. |
APA | Yang JQ.(2019).Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,478(2),1020-1026. |
MLA | Yang JQ."Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 478.2(2019):1020-1026. |
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