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In this paper, we generalize some regularity criteria for weak solutions of three-dimensional (3D) Boussinesq equations in homogeneous Besov spacesB˙(ℝ3)p,qs{\dot{{B}}{{}_{p,q}^{s}}(\mathbb{R}^{3})}and homogeneous Triebel–Lizorkin spacesF˙(ℝ3)p,qs{\dot{{F}}{{}_{p,q}^{s}}(\mathbb{R}^{3})}. We also deduce them for the homogeneous Sobolev spacesW˙pm⁢(ℝ3){\dot{W}^{m}_{p}(\mathbb{R}^{3})}in a certain sense. We show that the weak solution(ω,ϕ){(\omega,\phi)}is regular on]0,T]{]0,T]}for allT&gt;0{T&gt;0}if the velocity ω satisfies

Generalization of some regularity criteria for 3D Boussinesq equations in homogeneous Besov and Triebel–Lizorkin spaces