Abstract：The main purpose is to study the mathematical infiuences of physical mechanisms on the global smooth solution (or global weak solutions) to the n-dimensional incompressible Navier-Stokes equations, where the dimension n ≥ 2. For this purpose, we will accomplish the limits of the L2 norm (with a sharp rate) of all order derivatives of the global solutions as time approaches infinity. We will represent these limits as explicit as possible, in terms of physical mechanisms. The mathematical representations of the physical mechanisms will be given explicitly in the Introduction. Then the mathematical infiuences of the physical mechanisms can be studied very clearly. There may be potential impacts on long time rigorous scientific computations, numerical simulations and weather forecast. The ideas and methods developed in this paper may be applied to study many other model equations, such as
(A) the two-dimensional dissipative quasi-geostrophic equation
(B) a general Korteweg-de Vries-Burgers equation
(C) a general Benjamin-Bona-Mahony-Burgers equation
