Analyticity for the fractional Navier-Stokes equations in critical Fourier-Besov-Morrey Spaces with variable exponents

Abstract

In this paper, by using the Littlewood-Paley theory and the Fourier localization argument, we obtained the analyticity of the solution to the fractional Navier-Stokes equations in variable exponents Fourier-Besov-Morrey spaces when the initial data are small.