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 pri...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.展开更多
Combining Le Bris and Lions＇ arguments with Ambrosio＇s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diff...Combining Le Bris and Lions＇ arguments with Ambrosio＇s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.展开更多
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)
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.11101407)the Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)
文摘Combining Le Bris and Lions＇ arguments with Ambrosio＇s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.
