Abstract
In this paper, we obtain the attraction properties for the velocity variable of the 2D Boussinesq equations with viscosity and without heat diffusion in the sense of the strong topology of V V and prove that the weak sigma-attractor has a pancake-like structure, which answer partly some questions arising in Biswas et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), pp. 381–405] and enrich the structure of the weak sigma-attractor.
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