Local existence and blow-up criterion for the generalized Boussinesq equations in Besov spaces

被引：13

作者：

Qiu, Hua ^{[1
]}

Du, Yi ^{[2
]}

Yao, Zheng'an ^{[3
]}

机构：

[1] S China Agr Univ, Dept Appl Math, Guangzhou 510642, Guangdong, Peoples R China

[2] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[3] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2013年 / 36卷 / 01期

关键词：

generalized Boussinesq equations; regularity criterion; local existence; Littlewood-Paley decomposition; GLOBAL WELL-POSEDNESS; PARTIAL VISCOSITY; MHD EQUATIONS; REGULARITY; SYSTEM;

D O I：

10.1002/mma.2573

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the three-dimensional generalized Boussinesq equations, a system of equations resulting from replacing the Laplacian?-?? in the usual Boussinesq equations by a fractional Laplacian (?-??)a. We prove the local existence in time and obtain a regularity criterion of solution for the generalized Boussinesq equations by means of the LittlewoodPaley theory and Bony's paradifferential calculus. The results in this paper can be regarded as an extension to the Serrin-type criteria for NavierStokes equations and magnetohydrodynamics equations, respectively. Copyright (c) 2012 John Wiley & Sons, Ltd.

引用

页码：86 / 98

页数：13

共 50 条

[1] Local existence and blow-up criterion for the Euler equations in the Besov spaces
Chae, D
[J]. ASYMPTOTIC ANALYSIS, 2004, 38 (3-4) : 339 - 358
[2] Local existence and blow-up criterion for the Boussinesq equations
Chae, D
Nam, HS
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1997, 127 : 935 - 946
[3] Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type
Takada, Ryo
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2008, 8 (04) : 693 - 725
[4] Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type
Ryo Takada
[J]. Journal of Evolution Equations, 2008, 8 : 693 - 725
[5] A blow-up criterion for 3D Boussinesq equations in Besov spaces
Qiu, Hua
Du, Yi
Yao, Zheng'an
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 73 (03) : 806 - 815
[6] Local existence and blow-up criterion of Holder continuous solutions of the Boussinesq equations
Chae, D
Kim, SK
Nam, HS
[J]. NAGOYA MATHEMATICAL JOURNAL, 1999, 155 : 55 - 80
[7] BLOW-UP CRITERION OF SMOOTH SOLUTIONS TO THE MHD EQUATIONS IN BESOV SPACES
YUAN Baoquan (Graduate School
Department of Applied Mathematics and Informatics
[J]. Journal of Systems Science & Complexity, 2005, (02) : 277 - 284
[8] Local Existence and Blow-up Criterion of the Inhomogeneous Euler Equations
D. Chae
J. Lee
[J]. Journal of Mathematical Fluid Mechanics, 2003, 5 : 144 - 165
[9] On the blow-up criterion for the quasi-geostrophic equations in homogeneous Besov spaces
Zhang, Zujin
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (03) : 1038 - 1043
[10] Local Existence and Blow-up Criterion of the Inhomogeneous Euler Equations
Chae, Dongho
Lee, Jihoon
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2003, 5 (02) : 144 - 165

← 1 2 3 4 5 →