Decay of solutions to the three-dimensional generalized Navier-Stokes equations

Abstract

In this paper, we first obtain the temporal decay estimates for weak solutions to the three dimensional generalized Navier-Stokes equations. Then, with these estimates at disposal, we obtain the temporal decay estimates for higher order derivatives of the smooth solution with small initial data. The decay rates are optimal in the sense that they coincides with ones of the corresponding generalized heat equation. These results improve the previous known results to the classical Navier-Stokes equations.