Abstract: Based on the theory of variable exponent Fourier-Besov function spaces, we used Littlewood-Paley decomposition tools, Fourier localization methods and Banach contraction mapping principle. By establishing estimations for both linear and nonlinear terms, we proved the global well-posedness and the Gevrey class regularity of the solutions to the fractional Boussinesq-Coriolis equations in critical variable exponent Fourier-Besov spaces.

Key words: Boussinesq-Coriolis equation, variable exponent Fourier-Besov space, global well-posedness, Gevrey class regularity