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On the improved blow-up criterion for the 2D zero diffusivity Boussinesq equations with temperature-dependent viscosity

Abstract This paper examines the two-dimensional zero diffusivity Boussinesq equations with temperature-dependent viscosity in the whole space. Whether or not its classical solutions global in time existence is a difficult problem and remains open. The main goal of this paper is to establish several blow-up criteria. More precisely, it is proved that is the maximal time interval if and only if the viscosity satisfies or the vorticity satisfies As a direct application of the above results, several other blow-up criteria in the Besov spaces and the multiplier spaces are also established.