Fatima Ouidirne - Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
Achraf Azanzal - Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
Chakir Allalou - Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco
Mohamed Oukessou - Laboratory LMACS, FST of Beni-Mellal, Sultan Moulay Slimane University, Morocco

In this paper, we establish the global well-posedness result of the viscous primitive equations of geophysics in the critical Fourier-Besov-Morrey space with variable exponents \mathcal{F \dot{N}}_{p(\cdot),k(\cdot),q}^{۲-\frac{۳}{p(\cdot)}}(\mathbb{R}^{۳}), when the initial data are small and Pandtl number P=۱, we also show the Gevrey class regularity of the solution.

Fourier-Besov-Morrey spaces with variable exponents, viscous primitive equations of geophysics, global well-posedness, Gevrey class regularity