Global regularity for homogeneous periodic data with normalised pressure

Let $(u_0,0,T)$ be a smooth periodic set of data. Global regularity for homogeneous periodic data with normalised pressure. There exists a smooth periodic solution $(u,p,u_0,0,T)$ with the indicated data and with normalised pressure. In the homogeneous case this is equivalent to the corresponding homogeneous periodic global regularity formulation; the source does not resolve the conjecture.