Global regularity for periodic data with normalised pressure

Let $(u_0,f,T)$ be a smooth periodic set of data. A periodic solution has normalised pressure when its pressure satisfies the normalisation used in the periodic Navier–Stokes formulation. Global regularity for periodic data with normalised pressure. There exists a smooth periodic solution $(u,p,u_0,f,T)$ with the indicated data and with normalised pressure. The pressure normalisation restores local well-posedness and removes the Galilean-invariance issue; the global existence assertion remains unresolved in the source.