Global existence theorem for the 3-D generalized micropolar fluid system in critical Fourier-Besov-Morrey spaces with variable exponent

Abstract

In this paper, we consider the 3-D generalized micropolar fluid system in critical Fourier-Besov-Morrey spaces with variable exponent. Using the Littlewood-Paley theory and Banach fixed point theorem we establish the global existence result with the small initial data belonging to
$\mathcal{F \dot{N}}_{p(\cdot),h(\cdot),q}^{4-2\alpha-\frac{3}{p(\cdot)}}(\mathbb{R}^{3}).$