Global well-posedness of the incompressible fractional Navier-Stokes equations in Fourier-Besov spaces with variable exponents

摘要

We study the Cauchy problem of the fractional Navier-Stokes equations in critical variable exponent Fourier-Besov spaces F(B) over dot(p(.),q)(4-a alpha-3/p(.)). 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. (C) 2018 Elsevier Ltd. All rights reserved.