A class of rotational solutions for the N-dimensional incompressible Navier-Stokes equations

In this paper, we present a sufficient and necessary condition for the existence of a class of rotational exact solutions u=b(t)+A(t)x for general N-dimensional incompressible Navier-Stokes equations. Such solutions are global and can be explicitly expressed by appropriate formulae. Once the required matrix A(t) is chosen, the solution u is directly obtained.