Well-posedness and decay of solutions for three-dimensional generalized Navier-Stokes equations

In this paper, we study the generalized incompressible Navier-Stokes equations in R3. Based on the energy estimates and regularization of the initial data with the heat semigroup, we prove the well-posedness of solutions in H5−4α2(R3) provided that the H5−4α2(R3)-norm of initial data is sufficiently small. In addition, in contrast to the generalized heat equation, the upper bound of the time decay rate of solutions to the generalized Navier-Stokes equations is also established.