EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION  

作　　者：郭春晓 张景军 郭柏灵 

机构地区：[1]Department of Mathematics, China University of Mining and Technology (Beijing) [2]College of Mathematics, Physics and Information Engineering, Jiaxing University [3]Institute of Applied Physics and Computational Mathematics

出　　处：《Acta Mathematica Scientia》2013年第4期883-900,共18页数学物理学报（B辑英文版）

基　　金：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：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 eommu- 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.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 eommu- 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 Galerkinmethod decay of solutions 

分 类 号：O241.8[理学—计算数学]