Abstract : It is obtained that a localization of the vorticity direction coherence conditions for the regularity of the 3D shear thickening fluids to an arbitrarily small space-time cylinder. It implies the regularity of any geometrically constrained weak solution of the system considered independently of the type of the spatial domain or the boundary conditions.
Keywords : Localization, direction of the vorticity, non-Newtonian fluid
MSC numbers : Primary 35Q30, 76A05
Supported by : This work was financially supported by the Fundamental Research Funds for the Central Universities under grant: G2020KY05205