Temporal decay for the generalized Navier-Stokes equations

In this paper, we study the asymptotic behavior of solutions to the generalized incompressible Navier-Stokes equations partial derivative(t)u + (-Delta)(alpha)u + u .del pi = 0, divu = 0. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and we obtain the optimal time decay rates of the higher-order spatial derivatives of solutions both in the subcritical case alpha is an element of (1/2, 1] and the critical case alpha = 1/2 by using the Fourier splitting approach and the interpolation techniques. (C) 2016 Elsevier Ltd. All rights reserved.