Global Well-Posedness and Analyticity of the Primitive Equations of Geophysics in Variable Exponent Fourier-Besov Spaces

We consider the Cauchy problem of the three-dimensional primitive equations of geophysics. By using the Littlewood-Paley decomposition theory and Fourier localization technique, we prove the global well-posedness for the Cauchy problem with the Prandtl number P=1 in variable exponent Fourier-Besov spaces for small initial data in these spaces. In addition, we prove the Gevrey class regularity of the solution. For the primitive equations of geophysics, our results can be considered as a symmetry in variable exponent Fourier-Besov spaces.