Global well-posedness for the fractional magneto-micropolar equations in variable exponent Fourier–Besov spaces

We focus on the Cauchy problem of the three-dimensional fractional magneto-micropolar equations in this paper. For small initial data, we prove the global well-posedness result in variable exponent Fourier–Besov Spaces. Our method relies on the main tools such as the Littlewood–Paley decomposition and the Fourier-localization method. Moreover, we obtain the Gevrey class regularity and time decay rate estimate of the solution.