Dynamics of the g-Navier–Stokes equations

The 2D g-Navier–Stokes equations has the following form: with the continuity equation •(gu)=0,where g is a suitable smooth real-valued function. For the restricted function g, Roh showed the existence of the global attractors for the periodic boundary conditions. One note that we get the 2D Navier–Stokes equations for g=1. Therefore, in this paper we are interested in the behavior of the global attractors of the 2D g-Navier–Stokes equations as g→1 in the proper sense and will prove that the semiflows, generated by the projection of the solutions of the g-Navier–Stokes equations into the solution space of the Navier–Stokes equations, is robust at the global attractor of the Navier–Stokes equations with respect to g. For that, we will use the Robustness theorem developed by Sell and You