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The present paper is dedicated to the global well-posedness issue for theBoussinesq system with the temperature-dependent viscosity in $\mathbb{R}^2.$We aim at extending the work by Abidi and Zhang ( Adv. Math. 2017 (305)1202--1249 ) to a supercritical dissipation for temperature.

Global well-posedness for 2-D Boussinesq system with the temperature-dependent viscosity and supercritical dissipation