# Is the divergence free condition really necessary?

In the paper "Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation" (available at https://web.math.princeton.edu/~const/cwhigh11907.pdf), the condition $$\nabla\cdot u =0$$ is apllyed in the estimate of $$I_3$$.

My question is if this condition is really necessary.