Abstract
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 Schefferʼs one.
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