A blow-up criterion for 3D Boussinesq equations in Besov spaces

On the global regularity of N-dimensional generalized Boussinesq system

“…The case of (7) may be done similarly using (26) and (27). Thus, Gronwall's inequality completes the proof of Proposition 4.1.…”

“…2) In the case N = 3, the regularity criteria results have been obtained in [26], [27], [31], and [32] in the whole space and [14] in a bounded domain. Recently, extensions of regularity criteria results by reducing the number of vector components or directions of derivatives have been obtained for various fluid dynamics partial differential equations: [4], [5], and [21] in the case of the NSE, [6], [35] in the case of the MHD system and [34] in the case of active scalars.…”

The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces

“…Note: After the submission of this paper, we learned Qiu-Du-Yao [18], where the authors obtained results similar to the part of Theorem 1.1 by using similar methods.…”

On the regularity criterion for the 2D Boussinesq equations involving the temperature

“…Actually, various criteria for the Boussinesq equations both in two dimension and higher dimension have been obtained by considerable works (see e.g. [17,[21][22][23][24][25][26][27][28][29][30][31][32] and the references therein).…”