Bulletin of the
Korean Mathematical Society BKMS

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time $L^2-$decay rate of weak solutions, which reveals that $L^2-$decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

Keywords: fractional Navier-Stokes equations; Fourier splitting method; weak solution

MSC numbers: 35Q30, 76D03, 76D05