Global existence and exponential decay of strong solutions for the three-dimensional Boussinesq equations

[摘要] In this paper, we consider the global existence of strong solutions to the three-dimensional Boussinesq equations on the smooth bounded domain Ω. Based on the blow-up criterion and uniform estimates, we prove that the strong solution exists globally in time if the initial $L^{2}$-norm of velocity and temperature are small. Moreover, an exponential decay rate of the strong solution is obtained.

[学科分类] 电力

[关键词] Boussinesq equations;Blow-up criterion;Global strong solutions;Exponential decay rate