Two dimensional damped Boussinesq equations with a class of large initial data

In this paper, we obtain global well-posedness for the two dimensional (2D) damped Boussinesq equations with a new class of large initial data, which is the first work weakening the condition of θ0. The proof is based on some special structures of the equations and a new way to handle the pressure. Moreover, this work can be seen as the supplement of Wan [Commun. Math. Sci. 6, 1617–1626 (2017) and Discrete Contin. Dyn. Syst. A 39, 2709–2730 (2019)] and Wu et al. [J. Nonlineal Sci. 25, 157–192 (2015)].