Global almost regularity for homogeneous $H^1$ data

Let $(u_0,0,T)$ be a smooth homogeneous $H^1$ set of data. An almost smooth finite energy solution is smooth for positive times and has the stated continuous spatial and time-derivative extensions to the initial time. Global almost regularity for homogeneous $H^1$ data. There exists an almost smooth finite energy solution $(u,p,u_0,0,T)$ with the indicated data. This corrects the smooth-category formulation by allowing limited time regularity at $t=0$; the existence assertion remains open in the source.