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Remarks on global well-posedness of mild solutions to the three-dimensional Boussinesq equations
Yang JQ(杨佳琪)
Corresponding AuthorYang, Jiaqi(yjqmath@163.com)
Source PublicationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
2019-10-15
Volume478Issue:2Pages:1020-1026
ISSN0022-247X
AbstractRecently, 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.
KeywordBoussinesq equations Global well-posedness Mild solutions
DOI10.1016/j.jmaa.2019.05.063
Indexed BySCI
Language英语
WOS IDWOS:000475547900036
WOS KeywordTIME DECAY
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
Classification二类
Ranking1
Citation statistics
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/79474
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 杨佳琪.(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 杨佳琪."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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