An analogue scalar model for the Navier-Stokes equations

We discuss on a new scalar model whose properties are similar to the NS equations (it preserves scaling, the antisymmetry of the bilinear term and is invariant by translations and dilations) but contains a singular integral operator. We construct a global-in-time weak solution when initial data is in a critical Morrey-Campanato space and show that it also satisfies a local energy inequality comparable to Scheffer's one. (C) 2011 Publie par Elsevier Masson SAS pour l'Acadernie des sciences.