Global well-posedness of smooth solution to the supercritical SQG equation with large dispersive forcing and small viscosity

It is known that global well-posedness for the supercritical SQG equation remains open, even the smooth data. In this paper, motivated by the recent work Cannone et al. (2013), we provide a simpler approach to the proof of global well-posedness for the supercritical SQG equation with large dispersive forcing, even with small viscosity. As an application, we prove global well-posedness for the 2D dissipative Boussinesq equations with small viscosity and large background data.