EXISTENCE UNIQUENESS AND DECAY OF SOLUTION FOR FRACTIONAL BOUSSINESQ APPROXIMATION

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

Abstract

Abstract:

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.

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

CLC Number:

35Q35

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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