Abstract

We study the Cauchy problem of the fractional Navier–Stokes equations in critical variable exponent Fourier–Besov spaces FḂp(⋅),q4−2α−3p(⋅). We discuss some properties of variable exponent Fourier–Besov spaces and prove a general global well-posedness result which covers some recent works about classical Navier–Stokes equations.

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