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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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