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

Abstract

In this paper, temporal decay estimates for weak solutions to the three dimensional generalized Navier-Stokes equa- tions are established firstly. With these estimates at disposal, algebraic time decay for higher order Sobolev norms of small initial data solutions are obtained. The decay rates are optimal in the sense that they coincide with ones of the corresponding generalized heat equation.