Well-posedness and decay of solutions for three-dimensional generalized Navier–Stokes equations. (1st September 2018) - Duan, Ning
Abstract: In this paper, we study the generalized incompressible Navier–Stokes equations in R 3 . Based on the energy estimates and regularization of the initial data with the heat semigroup, we prove the well-posedness of solutions in H 5 − 4 α 2 ( R 3 ) provided that the H 5 − 4 α 2 ( R 3 ) -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.