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. Using the Fourier localization argument and Littlewood-Paley decomposition, we obtain the global well-posedness result for small initial data $(u_0,{\theta }_0)$ belonging to the critical variable exponent Fourier-Besov spaces $\mathcal{F}{\dot{\mathcal{B}}}_{p(\cdot ),q}^{2-\frac{3}{p(\cdot )}}$.