Global well-posedness for the 3D rotating Boussinesq equations in variable exponent Fourier-Besov spaces - Xiaochun Sun; Yulian Wu; Gaoting Xu (AIMS Mathematics, 2023)
We study the small initial data Cauchy problem for the three-dimensional Boussinesq equations with the Coriolis force in variable exponent Fourier-Besov spaces. Using the Fourier localization argument and Littlewood-Paley decomposition, we obtain the global well-posedness result for small initial data $ (u_0, θ_0) $ belonging to the critical variable exponent Fourier-Besov spaces $ \mathcal{F}\mathcal{\dot{B}}_{p(·), q}^{2-\frac{3}{p(·)}} $.