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Global well-posedness for 2-D Boussinesq system with the temperature-dependent viscosity and supercritical dissipation. (English) Zbl 1414.35153
Summary: The present paper is dedicated to the global well-posedness issue for the Boussinesq system with the temperature-dependent viscosity in $$\mathbb{R}^2$$. Motivated by the work [H. Abidi and P. Zhang, Adv. Math. 305, 1202–1249 (2017; Zbl 1353.35220)] on the critical dissipation $$\kappa | D |^\alpha \theta$$ with $$\alpha = 1$$ in the temperature equation of the system, we consider the extension of their work to the supercritical dissipation for $$2 / 3 < \alpha \leq 1$$.

##### MSC:
 35Q30 Navier-Stokes equations 35Q35 PDEs in connection with fluid mechanics 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 42B25 Maximal functions, Littlewood-Paley theory
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