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.

Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent

In this paper, we consider the generalized porous medium equation. For small initial data u0 belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using the Fourier localization principle and the Littlewood-Paley decomposition technique. Furthermore, we also show Gevrey class regularity of the solution.