Well-posedness and analyticity for the viscous primitive equations of geophysics in critical Fourier-Besov-Morrey Spaces with variable exponents

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.

Keywords:

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