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

This is a remark that by using an adaptation of the technique invented by A. Kiselev, F. Nazarov, and A. Volberg, 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 bounded in space and time, and a-Holder continuous in space, alpha > 0. In particular, this improves the assumptions on both the initial data and the force in the result by S. Friedlander, N. Pavlovic, and V. Vicol. (C) 2017 Elsevier Inc. All rights reserved.