Global Well-Posedness for the 3D Rotating Boussinesq Equations in Variable Exponent Fourier-Besov Spaces

We study the small initial data Cauchy problem for the three-dimensional Boussinesq equations with the Coriolis force in variable exponent Fourier-Besov spaces. By 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 $\mathcal{F}\mathcal{\dot{B}}_{p(\cdot),q}^{2-\frac{3}{p(\cdot)}}$.