Global regularity for the critical 2-D dissipative quasi-geostrophic equation with force

Abstract

This is a remark that by using an adaptation of the technique invented by A. Kiselev, F. Nazarov, and A. Voldberg, with a modified scaling argument, we can prove global regularity of the critical 2-D dissipative quasi-geostrophic equation with smooth periodic force, under the assumption that the initial data is smooth and periodic, and the force is $\alpha$-H\"older continuous in space, $\alpha > 0$.