We investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the 3D incompressible Navier-Stokes and Euler systems. Under the suitable assumption on G. Lame coefficients, we establish the global well-posedness of the Cauchy problem for the 3D incompressible Navier-Stokes and Euler equations for a new class of the smooth large initial data in orthogonal curvilinear coordinate systems. Moreover, we also establish the existence, uniqueness and exponentially decay rate in time of the global smooth solution to the initial boundary value problem for the 3D Navier-Stokes equations for a class of the smooth large initial data and a large class of the special domain in orthogonal curvilinear coordinate systems. Moreover, the related problems on the axisymmetric Navier-Stokes equations are surveyed and some results on the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations will also be reviewed.