Global well-posedness of the incompressible fractional Navier–Stokes equations in Fourier–Besov spaces with variable exponents. (15th February 2019) - Ru, Shaolei; Abidin, Muhammad Zainul
Abstract: We study the Cauchy problem of the fractional Navier–Stokes equations in critical variable exponent Fourier–Besov spaces F B ̇ p ( ⋅ ), q 4 − 2 α − 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.