Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1415-1427.

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Asymptotic Behavior for the Damped Boussinesq

Xiaojing Cai*(),Yanjie Zhou   

  1. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048
  • Received:2020-07-21 Online:2021-10-26 Published:2021-10-08
  • Contact: Xiaojing Cai
  • Supported by:
    the National Key Research and Development Project(2017YFC1500301);the Joint Key Project of the NSFC and the China Earthquake Administration(U1839206);the Research Foundation for Advanced Talents of Beijing Technology and Business University(19008020161)


This paper mainly focus on the asymptotic behavior of the solutions for the 3D Boussinesq equations with damping term. We obtain the explicit time decay rate of the solutions by means of the Fourier splitting method. In addition, we get the upper-bound of the time decay results compared with the heat equation.

Key words: Boussinesq Equations, Damping term, Fourier Splitting Method, Decay

CLC Number: 

  • O175.29