Global Large Solution to Navier-Stokes and SQG Equations with Time Oscillation

In this paper, we consider the model of 3D incompressible Navier-Stokes equations and 2D supercritical Surface Quasi-Geostrophic equations with time oscillation in the nonlinear term. We obtain that there exists global smooth solution of these two equations for any initial data $u_0\in H^2$.