EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION

doi:10.1016/S0252-9602(13)60048-X

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 883-900.doi: 10.1016/S0252-9602(13)60048-X

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EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION

郭春晓*|张景军|郭柏灵

Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China； College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, China； Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, China

收稿日期:2012-04-09 修回日期:2012-10-18 出版日期:2013-07-20 发布日期:2013-07-20
通讯作者: 郭春晓，guochunxiao1983@sina.com E-mail:guochunxiao1983@sina.com
基金资助:
Sponsored by the Fundamental Research Funds for the Central Universities (2010QS04); the National Science Foundation of China (11201475, 11126160, 11201185); Zhejiang Provincial Natural Science Foundation of China under Grant (LQ12A01013).

EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION

GUO Chun-Xiao*, ZHANG Jing-Jun, GUO Bo-Ling

Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083, China； College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, China； Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, China

Received:2012-04-09 Revised:2012-10-18 Online:2013-07-20 Published:2013-07-20
Contact: GUO Chun-Xiao，guochunxiao1983@sina.com E-mail:guochunxiao1983@sina.com
Supported by:
Sponsored by the Fundamental Research Funds for the Central Universities (2010QS04); the National Science Foundation of China (11201475, 11126160, 11201185); Zhejiang Provincial Natural Science Foundation of China under Grant (LQ12A01013).

摘要/Abstract

摘要：

The Boussinesq approximation finds more and more frequent use in geologi-cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of commu-tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results
obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.

关键词: fractional Boussinesq approximation, commutator estimate, Galerkin method, decay of solutions

Abstract:

Key words: fractional Boussinesq approximation, commutator estimate, Galerkin method, decay of solutions

中图分类号:

35Q35

郭春晓, 张景军, 郭柏灵. EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION[J]. 数学物理学报(英文版), 2013, 33(4): 883-900.

GUO Chun-Xiao, ZHANG Jing-Jun, GUO Bo-Ling. EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION[J]. Acta mathematica scientia,Series B, 2013, 33(4): 883-900.

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EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION

EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION

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