Abstract
In this paper we consider the following 2D Boussinesq–Navier–Stokes systems
with ν > 0, κ > 0 and 0 < β < α < 1. When \({\frac{6-\sqrt{6}}{4}({\doteq}0.888) < \alpha < 1, 1-\alpha < \beta \leq f(\alpha)}\), where f(α) < 1 is an explicit function as a technical bound, we prove the global well-posedness results for the rough initial data.
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Miao, C., Xue, L. On the global well-posedness of a class of Boussinesq–Navier–Stokes systems. Nonlinear Differ. Equ. Appl. 18, 707–735 (2011). https://doi.org/10.1007/s00030-011-0114-5
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DOI: https://doi.org/10.1007/s00030-011-0114-5