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

Abstract

Abstract 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 $L^{2}$ -norm of velocity and temperature are small. Moreover, an exponential decay rate of the strong solution is obtained.

Keywords

• Boussinesq equations
• Blow-up criterion
• Global strong solutions
• Exponential decay rate