Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations | |
Yang JQ(杨佳琦) | |
Source Publication | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
2019-10-15 | |
Volume | 478Issue:2Pages:1020-1026 |
ISSN | 0022-247X |
Abstract | 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. |
Keyword | Boussinesq equations Global well-posedness Mild solutions |
DOI | 10.1016/j.jmaa.2019.05.063 |
Indexed By | SCI |
Language | 英语 |
WOS ID | WOS:000475547900036 |
WOS Keyword | TIME DECAY |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
Classification | 二类 |
Ranking | 1 |
Contributor | Yang, Jiaqi |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://dspace.imech.ac.cn/handle/311007/79473 |
Collection | 流固耦合系统力学重点实验室 |
Recommended Citation 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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