Global well-posedness and asymptotic behavior for the 2D Boussinesq system with variable viscosity

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D Boussinesq system with variable kinematic viscosity depending on the temperature. Comparing with the previous results given by Abidi and Zhang [4] who considered the critical case alpha = 1, we weaken the dissipation effect in the temperature equation to the supercritical case alpha is an element of (0, 1). Furthermore, we obtain the algebraic decay estimate for parallel to u parallel to(L2). (C) 2019 Elsevier Inc. All rights reserved.