New results of general n-dimensional incompressible Navier–Stokes equations

Let u=u(x,t,u0) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier–Stokes equations where the spatial dimension n 2, 0 ε 1 is a constant and is a constant vector. Note that if ε=0 and β=0, then the problem reduces to the traditional Navier–Stokes equations. Let the scalar functions , , i,j {1,2,…,n}. Define the real vector-valued functions Φi=( i1, i2,…, in)T. Let the initial data satisfy Then For any integer m 1, we will establish the following limit This kind of exact limit will have great influence on the Hausdorff dimension of the global attractor of the model equations.